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A Highly Reliable Embedded Optical Torque Sensor Based on Flexure Spring

A Highly Reliable Embedded Optical Torque Sensor Based on Flexure Spring Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 4362749, 14 pages https://doi.org/10.1155/2018/4362749 Research Article A Highly Reliable Embedded Optical Torque Sensor Based on Flexure Spring 1 2 3 1 3 Yuwang Liu , Tian Tian, Jibiao Chen , Fuhua Wang, and Defu Zhang State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, China Department of Mechanical Engineering, Shenyang Ligong University, Shenyang, China Department of Mechanical Engineering, Northeastern University, Shenyang, China Correspondence should be addressed to Yuwang Liu; liuyuwang@sia.cn Received 23 October 2017; Revised 2 January 2018; Accepted 28 January 2018; Published 15 April 2018 Academic Editor: QingSong He Copyright © 2018 Yuwang Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We propose a new highly reliable and lightweight embedded optical torque sensor for biomimetic robot arm enabling the torque measurement in joints, which can measure torque of the joint by detecting torsion of its elastic element (mechanical structure or flexure element). Flexure spring is introduced as the elastic element of the torque sensor in this paper. Because of its curve modeling, flexure spring is not inclined to be broken contrast to crossbeam structure, which is commonly used in torque sensor. Thanks to this structure, we can build a torque sensor as an extremely compact and highly reliable size. Six types of flexure spring are proposed to be used as the elastic element of the torque sensor in this paper, which have the potential for the requirements of measurement range and multidimensional detection. The optical electronic, less influenced by electromagnetic interferences, is selected to measure the torsion displacement of the flexure spring. The proposed design is analyzed, which can obtain the successful measurement of the torque with a load capacity of 1 Nm. One of the designed optical torque sensors is optimized by FEM. The calibration and experiment are conducted to ensure its feasibility and performance. 1. Introduction Kang et al. [4] designed a mechanically decoupled six- axis force/torque sensor. It is a crossbeam sensor, which use This paper focuses on the design of a new highly reliable and strain gauge technique to detect force/moment. The size of lightweight embedded optical torque sensor for biomimetic this sensor is small with thickness of 37 mm, and the robots in order to ensure accuracy and stability while perform- maximum torque detected by this sensor is 40 Nm. Also, ing practical tasks of physical interaction with unstructured Ma et al. [5] presented three kinds of compact torque sensors using strain gauge technique. The structure of these sensors is environment. Biomimetic robot arm is used to realize dexter- ous taskssuch asinteractionwith human or manipulation with cartwheel flexure, which is also crossbeam. The measurement objects in hazardous conditions. To achieve the stability in ranges of these sensors are 7 Nm, 22 Nm, and 50 Nm, respec- contact with environment and realize safety while performing tively. The thickness is about 6 mm which is much suitable for tasks of physical interaction with human and unstructured using an embedded application. However, it is difficult to environment, it is essential to calculate the torque of each joint attach the strain gauge to the structure reliably while develop- of the robot arm. The torque information of the torque sensor ing the type of torque sensor which is commonly sensitive to greatly enhances the force perception ability of biomimetic electrical noise and temperature. Kim et al. [7] designed a robot joint. The development of embedded torque sensor, six-axis force/moment capacitive sensor using dielectric especially, a lightweight and highly reliable one, has been of elastomer. Its deformation results in variation of capaci- great interest for decades [1–3]. Based on its measurement tance, which is used for sensing force/moment. The size methods, the torque sensor can be classified as strain gauges of this sensor is 67 mm × 30 mm, and the measurement [4–6], capacitive [7–9], piezoelectric [10, 11], photoelectric range is 0.16 Nm. However, it is generally nonlinearity. [1, 12–17], and so on [18, 19]. Liu et al. [10] designed a no-elastic six-axis force/moment 2 Applied Bionics and Biomechanics irregular-shaped objects and has flexible obstacle avoidance sensor using piezoelectric. The maximum torque detected by this sensor is as high as 250 Nm when the size is small performance. a i = 1~7 are under-actuated joint units in as 50 mm × 30 mm. However, piezoelectric sensor is gener- the robSSot. Each under-actuated joint unit is made up of a ally too stiff for this condition. scissor mechanism, an elastic device, bottom links, and sup- Recently, lots of researchers have been interested in this port links. The robot is directly driven by a single motor. type of optical for its compact size, noncontact approach, Therefore, the output torque of the driving motor has a great and less electromagnetic interference. Kim et al. [12] influence on the holding stability of the robot. In Figure 1, (a) designed a three-axis force/moment optical sensor using is the torque sensor and (b) is the driving motor. The crossbeam which has a thickness of 7 mm and a diameter of inner ring of the sensor is fixed with the driving motor, 28 mm making it the most compact. Also, Shams et al. [13] and the outer ring is fixedly connected with the robot. presented an optical crossbeam torque sensor. This sensor The torque sensor we designed can accurately measure is compact with a thickness of 11 mm and a diameter of the output torque of the motor. Therefore, the torque sen- 80 mm. Tsetserukou et al. [14] proposed three types of opti- sor can be well applied to a biomimetic actuation similar cal torque sensors. The first one is the cross-shaped spring to the elephant’s trunk robot and is of great significance with a diameter and thickness of 30 mm which can be used for studying the stability and performance characteristics to detect 1.75 Nm load. The second one is the hub spoke- of a bionic robot system. shaped spring with a diameter of 42 mm and thickness of Six types of flexure spring are proposed to be used as the 6.5 mm, and the sensor can be used to measure torque up mechanical structure. And the proper optical electronic is to 0.8 Nm. The third one is the ring-shaped spring with a selected to measure the torsion of the flexure spring. As a diameter of 42 mm and thickness of 10 mm, which can be result, six typical torque sensors are designed in Section 2. used to handle torque up to 0.8 Nm. Simulations of all the six types of torque sensor were done Relatively speaking, the optical torque sensors tend to by FEM (finite element method) software ANSYS, which acquire much more deformation which is very suitable to are described in Section 3. Simulation results show that build a biomimetic robot. However, the proposed sensors 2-rib torque sensor under 1 Nm load covers the measure- are commonly close to the yield stress at the maximum of ment range of the selected optical electronic perfectly. torque size in which the overload protection needs to be The 2-rib torque sensor is selected to be further studied. added to keep it operating. However, it is inconvenient to And topology optimization of this sensor is represented build a sensor with this mechanism as it will increase the joint in Section 3. The 2-rib optical torque sensor is calibrated, size. Factor of safety is a property to evaluate the ability of and several experiments (linearity, hysteresis, and repeat- resistance to overload. It suggests the property of reliability, ability) are conducted in Section 4. which is equal to the yield stress divided by the allowed one. However, an ideal compact size of the structure with a high 2. Sensor Design factor of safety especially for the embedded sensor is very Torque sensor can be divided into two main parts, elastic ele- hard to acquire. The fact is that the factor of safety of optical ment and sensing element. Elastic element produces torsion torque sensors is generally limited to 1.0~2.0 [1, 14, 15, 34]. under the load of torque. The deformation accuracy is Flexure spring, also called planer spring or torsion spring, detected and measured by the sensing element (Figure 2). has been used in many fields for its advantages of compact Thus, the applied torque could be acquired by establishing structure and highly reliable performance [20–25]. It has the relationship between the torque and the torsion. been used to design a strain gauge sensor [22, 23]. However, the application of flexure spring to torque sensor has not 2.1. Sensing Element Design. As the input of torque sensor is been developed yet. In addition, limited to the mount space, usually connected to motor [26, 27], the optical technique there is also a challenge to build an optical torque sensor less influenced by electrical noise is preferred. In many types based on the spring. of optical detection, we decided to use ultrasmall size of In this paper, we develop a highly reliable embedded photointerrupter as sensitive element to measure the rela- optical torque sensor using flexure spring. The size of the tor- tive motion of sensor’s component. In those products, que sensor is designed to be extremely small, according to RPI-131 and RPI-121 are considered as their wide mea- that of joint with the output of 1 Nm. The flexure spring, with surement range and small size. Although its size is slightly the ability of storing energy and reducing the potential of large, we finally selected RPI-131 to obtain a wide mea- stress concentration, is applied to realize the high reliability surement range. The dimension of selected photointerrup- of torque sensor. In [33], we imitate an elephant’s trunk with ter is 4.2 mm × 4.2 mm × 5.2 mm, the measurement range is the special function of holding objects and propose a new about 0.6 mm, and its weight is only 0.05 g. type of shape-adaptive elephant’s trunk robot to which the embedded optical torque sensor could be well applied. As 2.2. Elastic Element Design. The performance of elastic ele- shown in Figure 1, the elephant’s trunk robot could be seen ment widely varies according to its material and configuration. as a biomimetic elephant’s trunk, whose effect could be equivalent to a kind of large artificial muscle. The robot 2.2.1. Material. Steel, aluminum, and titanium are general consists of a base and some under-actuated joint units; the materials used in the design of torque sensor. Although the size of which is very similar to the real trunk. In an unstruc- yield stress of aluminum is the smallest, we select it because tured environment, the robot can adaptively grab various its density is half of steel and 2/3 of titanium. Also, aluminum Applied Bionics and Biomechanics 3 (a) (b) Figure 1: Elephant’s trunk robot and torque sensor. (a) Elephant’s trunk robot; (b) application of torque sensor in biomimetic actuation. Elastic element Detection Torque deformed sensing application Torque size Establishment Signal acquiring relationship processing Figure 2: Working principle of torque sensor. is the most economical among these materials. As a result, the aluminum 7075 with yield of 500 MPa is selected to man- Table 1: Parameters of the torque sensor. ufacture the elastic element of torque sensor. Item Parameter Item Parameter Diameter 60 mm Mount 11 mm 2.2.2. Configuration. Two types of shapes, namely, axis struc- Thickness 4 mm Inner/outer flange ϕ 3 mm/ϕ 2.5 mm ture and crossbeam, are generally used in elastic element Hole 12 mm design. The axis structure is usually used to load big torque because of its highly reliable performance and its capability to reduce coupling [3, 14, 28, 29]. However, it is difficult to 4 Applied Bionics and Biomechanics be assembled into small space of a joint. On the other hand, The built physical model can be seen in Figure 3. the crossbeam is widely used because of its compact structure The work done in deflecting the sensor Δθ by torque T is and good linearity [1, 4, 5, 7, 12–16]. However, it tends to 1/2TΔθ, and for these parts, the stored energies due to produce stress concentration and even fail. torsion are U , U , and U . Therefore, 1 2 3 Flexure spring has been gradually applied in many fields such as cryocoolers [20, 21], sensors [22–24], and U = U + U + U = TΔθ 2 1 2 3 geophones [25] because of its compact structure and highly reliable performance. Contrast to the crossbeam, In this model, we accept the equivalent force F and this structure could be more flexible which is beneficial moment M stand for the applied torque T. They are to the requirement of the relatively wide deformation. In F = , this section, the elastic element design is configured based NR out on the flexure spring. M = FR − R , Because of the variety of the number and angle of ribs, the 0 out 1 configuration would have potential for different measure- where N denotes the number of ribs. For part I, we can ment ranges. Theoretically, the number of ribs could be calculate the normal force F and tangential force F as 11 12 any. However, one to six ribs are considered feasible. The F = F cos α , designed parameters of the torque sensor are mainly deter- 11 1 mined by the robot joint, whose maximum output torque is F = F sin α , 12 1 1 Nm. These parameters are shown in Table 1. And the six typical configurations are shown in Table 2. where α is the angle between F and horizontal. Therefore, the stresses are 2.3. Integration. The interrupter shield and bracket were F F xy M y 11 12 0 designed to vary the intensity of light and support the photo- σ = + + , 1x A I I interrupter, respectively. The interrupter shield is attached to σ =0, rib while bracket is attached to outer ring (shown in Table 2). 1y Obviously, we can find that the multirib configurations have 3 F 2y a wide measurement range and multidetection, while the sen- τ = 1 − , 1xy 2 A b sitivity is much lower. where A is the sectional area, which can be calculated as 3. Analysis A = b ⋅ h (h is the thickness and b is the wide). I is the moment of inertia, which is equal to b h/12. Due to In this section, the stiffness equations of the proposed con- figurations are deduced. With FEM simulation using the U = σεdV, 6 software of ANSYS, the theory is examined by building the relationship between design angle and stiffness. The optimal structures in these six typical configurations are where ε is the strain displacement. We can acquire the energy of part I as selected according to their analysis results. Through the opti- mization of topology also using ANSYS, we finally acquired 1 σ the ideal configuration. 1xy 1x U = σ ε dV = dV + dV 1 1 1 2 2E 2G 3.1. Physical Modeling. The stiffness k means the required F F xy M y 1 torque to produce a unit angle and can be calculated from 11 12 0 = + + dV A I I 2E k = T/Δθ = TR /Δs, 1 2 out 2 9 F 2y + 1 − dV 8 b GA where T is the applied torque, Δθ is the deformed revolving 2 2 3 2 2 2 F L F L M L F M L 3F L angle, R is the radius of out flange, and Δs is the produced 11 1 12 1 0 1 12 0 1 12 1 out = + + + + , tangential displacement. While T and R are given, the core 2EA 6EI 2EI 2EI 5GA out issue is to acquire the formula of torsion in these sensors. To complete it, several assumptions and simplified physical where E is the modulus of elasticity, G is the modulus of rigidity, L is the distance between point A and B x , y . model are needed. Assumptions 1 1 1 For part II, in any point P x , y of the ribs, it has (1) during the deformation, the cross section remains V = F cos α , initial conditions; N = F sin α , (2) for the selected Al-7075, the material of the beam is homogeneous; M = −F y − y + F x − x + M , P 11 12 2 1 1 2 1 (3) when the deformation is small, the calculation can be where V, N, and M are the tangential force, normal force, seen as linearly elastic. and moment size in point P, respectively. α is the angle 2 L Applied Bionics and Biomechanics 5 Table 2: Six typical configurations. Number of ribs 1 2 3 Shield Bracket Mount Photointerrupter Hole Diameter Configuration Rib2 Rib1 Inner flange Outer flange M , F , and F Multidetection M /F M , F z x y z x z x Number of ribs 4 5 6 Configuration M , F , and F M , F , and F M , F , and F Multidetection z x y z x y z x y L z Cross section M R (a) Part II P(x, y) F‵ 12 F x Part I Part III D C M 11 M 0 2 (b) (c) (d) Figure 3: Physical model of the torque sensor: (a) overall appearance; (b) part I; (c) part II; (d) part III. 6 Applied Bionics and Biomechanics Table 3: Results of finite element analysis. Ribs Structure Displacement Stress Results Max displacement 4.0835 deg Max stress 157.32 Mpa Max displacement 0.3097 deg Max stress 65.627 Mpa Max displacement 0.0272 deg Max stress 17.55 Mpa Max displacement 0.0134 deg Max stress 11.767 Mpa Max displacement 0.0074 deg Max stress 6.9949 Mpa Max displacement 0.0049 deg Max-stress 5.8602 Mpa 4.5 0.1 0.05 3.5 −0.05 2.5 −0.1 −0.15 1.5 −0.2 −0.25 0.5 0 −0.3 12 3 4 5 6 12 3456 Ribs Ribs Angle from equation Error Anglefrom FEM FEM (a) (b) Figure 4: Relationship between deformation and the number of ribs: (a) deformation; (b) error. Deformation (deg) Deformation (deg) Applied Bionics and Biomechanics 7 between F and V, which can be calculated as α = pi − θ − α . 2 1 A: Shape optimization is the moment in point B, which is equal to M + F L . Figure 1 0 12 1 Type: shape finder As the rib is the curve beam, the expression according to Unit: t the method of energy is given in [30] Time: 0 2014/9/23 15:57 2 2 2 M kV R N R M N P P U = dθ + dθ + dθ − dθ 9 2AEe 2AG 2AE AE Max or Min U = U + U + U + U , 10 2 21 22 23 24 where k is a factor depending on the form of the cross section (for regular section which is equal to 1.2), e is the distance from the centroidal axis to the neutral axis, e = R − b/ ln R + b/2 − ln R − b/2 , and θ is the angle from axis of x to point P. Therefore, we can separately cal- Remove culate the energy of U i =1,2, 3,4 as 2i Marginal M 1 2 Keep U = dθ = −F y − y + F x − x + M dθ, 21 11 2 1 12 2 1 1 2AEe 2AEe 2 2 Figure 5: Result of optimization. kV R kF R U = dθ = cos θ + α dθ, 22 1 2AG 2AG where M is the moment in point C, which is equal to F R 2 2 2 12 N R F R U = dθ = sin θ + α dθ, cos α − cos θ − F R sin θ − sin α + M . θ is the angle 23 1 3 0 11 0 3 1 0 2AE 2AE of the rib. The energy of part III can be calculated as M N F U = − dθ = −F y − y + F x − x + M sin θ + α dθ, 24 11 2 1 12 2 1 1 1 AE AE 3xy U = σ ε dV + dV 11 3 3 3 2 2G F F xy M y 1 9 F 31 32 2 where the coordinates of point B x , y and point 1 = − + dV + A I I 2E 4 GA P x , y are 2 2 2y x = −R cos α , 1 3 1 − dV y = R sin α , 1 3 2 2 3 2 2 2 F L F L F M L M L 3F L 31 2 32 2 32 2 2 2 2 32 2 = − − + + x = −R cos θ, 2EA 6EI 2EI 2EI 5GA y = R sin θ 15 Therefore, we can find the Δθ as For part III, we can calculate the normal force F and tangential force F as 32 2 U + U + U 1 2 3 Δθ = 16 F = F sin α , 31 4 And the stiffness can be obtained as F = F cos α , 32 4 k = 17 Δθ According to these formulations, we could make the where α is the angle between F and horizontal in this part, which can be calculated as α = α + θ − pi. Therefore, the conclusion that the stiffness of k is in proportion to the 4 1 0 ribs number of N, modulus elasticity of E, and thickness stresses in this part are of h. F F xy M y 31 32 2 + , σ = − 3x 3.2. FEM Static. The six typical configurations are analyzed A I I by using ANSYS. In the analysis, the mesh type is hexahe- σ =0, 3y dron element, and each model comprises approximately 35,000 elements and 140,000 nodes. A fixed constraint is 3 F 2y τ = 1 − , applied to the inner flange, and a torque load of 1 Nm is 3xy 2 A b applied to the outer flange. The analysis results are listed in 8 Applied Bionics and Biomechanics 0.14959 max 0.00133 max B: static structural B: static structural Figure Figure 0.13297 0.0011822 Type: equivalent elastic strain z M Type: total deformation Unit: mm/mm Unit: mm Time: 1 Time: 1 0.11635 0.0010344 2015-11-19 19:59 2015-11-19 19:59 0.099725 0.099725 Max 0.00088667 0.083105 Min 0.00059111 0.066484 Min 0.00044334 0.049863 0.00029556 0.033242 0.00014778 0.016621 Max 2.2587e − 9 min 0 min (a) (b) 91.759 max 15 max B: static structural Figure B: static structural Type: equivalent (von Mises) stress M 81.564 z Figure Unit: MPa Type: safety factor Time: 1 71.368 Time: 1 2015-11-19 19:59 10 2015-11-19 19:59 61.173 Min Max 50.978 Max 5.449 min 40.782 Min 30.587 20.391 10.196 0.00013769 min (c) (d) 0.12997 max 46.978 max C: static structural C: static structural Figure Figure 0.11553 41.758 Type: total deformation Type: Equivalent (von Mises) stress Unit: mm Unit: MPa x Time: 1 Time: 1 0.10109 36.538 2015-9-29 16:10 2015-9-29 16:10 0.086648 31.318 0.072207 26.099 Min 0.057765 20.879 Min 0.043324 15.659 Max 0.028883 10.439 Max 0.014441 5.2197 0 min 3.681e − 6 min (e) (f) Figure 6: FEA results of optimized structure: (a) deformation from M ; (b) strain from M ; (c) stress from M ; (d) factor of safety from M ; z z z z (e) deformation from F ; (f) stress from F . x x Table 3. The relationship of displacement with those 6 when the number of ribs increased. The maximum stress configurations as FEM and formulae is shown in Figure 4. of 157.23 MPa was less than the material yield stress of The displacement of the applied torque of the elastic 500 MPa. Therefore, in this condition, the stress was not element was reduced from 2.1381 mm to 0.0025852 mm the core issue to consider. Finally, the 2-rib structure Applied Bionics and Biomechanics 9 was found to be optimal because the deformation of one Table 4: Comparison of performances of original and optimized structure. rib was beyond the measurement range of RPI-131, while the deformation of others was significantly small. Furthermore, Item Original Optimized the displacement of 0.1627 mm was detectable using the 34,000 elements, 60,000 elements, RPI-131. Mesh 136,000 nodes 11,000 nodes Displacement 0.16086 mm 0.14959 mm 3.3. FEM Optimization. Optimization was measured to deter- Max stress 64.567 MPa 91.759 MPa mine the optimal structure. The topology optimization to Max strain 0.00089679 mm 0.00133 mm achieve the lightest weight was conducted using ANSYS with the reliability constraints and stress limitations. An efficient Factor of safety 7.7439 5.449 method for topology optimization is reducing the quality Mass 15.442 g 13.72 g and volume to make the model approach the optimized tar- get. In this case, the mechanical performance should be partly retained. In the analysis, the solid element was accepted. Approxi- 4.1. Experiment Preparation. The sensor, discussed in this mately 90,000 elements and 160,000 nodes were produced in paper, is manufactured with a computer numerical control the meshing. Similarly, a fixed constraint was applied to the milling machine (Figure 8), and the test system (Figure 9) is inner flange, and the torque was loaded at the outer flange. built to study its performances. Figure 10 shows the estab- The quality of the target optimization was set to half. lished experiment circuit. The photointerrupter is composed Figure 5 shows that the red area could be removed without of an infrared light emitting diode (LED) at one side and a significantly affecting the performance in mechanics. transistor (detector) at the other side (shown in Based on the result of optimization, we finally acquired Figure 10(a)). The graph in Figure 10(b) shows there is a the ideal configuration by modelling with the method of linear relationship between the distance and the current eccentric circle to approach the optimization results. To eval- of the collector. According to this linear relationship, uate the performance of the optimized 2-rib configuration, acquiring the applied torque size by detecting shield displace- the static analysis was reconducted. In the analysis, the solid ment would be successful. Considering the sensitivity, U = element was also accepted, and approximately 54,000 ele- 10 V and R =10 kΩ were selected [13]. R = 833Ω was cho- L 0 ments and 98,000 nodes were produced. The same torque sen for I ≈ U − U /R = 10V − 1 16 V /833Ω =10 4mA d 0 load and fixed constraint were applied on the outer and inner (where U ≈ 1 16 V that is the voltage drop caused by LED). flanges, respectively. As this sensor is immune to the loads of Channels A and B were linked to the oscilloscope channels 1 M , M , F , and F (the deformation from these loads could x y y z and 2, respectively. In this kind of circuit, the maximum out- not be detected by the photointerrupters), the influence by F put voltage was 9.8 V, and the output voltage in the initial posi- needs to be considered. In the analysis, the force load (15 N) tion was approximately 4.5 V. and fixed constraint were also applied on the outer and inner flanges, respectively. Figure 6 shows the analysis 4.2. Linearity. Linearity describes the degree offset between results of the optimized 2-rib structure. The comparison the actual line and ideal straight line [31, 32]. The torque of performances between the original and optimized struc- is achieved (from 0 Nm to 0.98 Nm) by placing load at the tures is listed in Table 4. lever of the test system, and the increased torque is According to (a) to (f) in Figure 6, we can obviously find 0.098 Nm. The experiment is conducted more than 50 that under the load of M , the deformations detected by the times to ensure the acquired data truly reflect the perfor- two photointerrupters are identical. While, under the load mance of the sensor. The experiment data are recorded of F , the deformations detected by the two photointer- in Table 5, and the graphs of linearity and error are drawn rupters are opposite. Therefore, the error caused by F , in Figure 11. With using polyfit function of MATLAB, the in a certain range, could be eliminated through the simple relationship between displacement and applied torque can signal process such as be average. Eventually, the designed be built as sensor could detect the torque of M without influence from other loads. Δ = −3 0198T +4 3250, 18 And through the topology optimization, the results show that the displacement was reduced by 7.01%, and the mass was reduced by 11.15%; meanwhile, the factor of safety was where Δ is the output voltage and T is the applied torque size. also reduced by 29.63%. Theoretically, the linearity of this The nonlinearity and torque sensitivity are expressed as sensor can be seen in Figure 7. ΔL 0 0986 max γ = × 100% = × 100% = 3 27%, 4. Experiments and Results FS 4 325 − 1 3052 ΔY 4 4118 − 1 4038 The performances of linearity, hysteresis, and repeatability S = = =3 07 V/Nm, ΔX 0 98 are important in evaluating the feasibility of the design of torque sensor. 10 Applied Bionics and Biomechanics −4 ×10 0.35 1.5 0.3 0.25 0.5 0.2 0.15 −0.5 0.1 −1 0.05 −1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Torque (Nm) Torque (Nm) Analysis results Error Fitted curve Ideal (a) (b) Figure 7: Simulation in the range of 0~1 Nm: (a) relationship of torque and displacement; (b) error. 4.4. Repeatability. Repeatability is usually necessary when Shield Photointerruper-A Flexure an unsteady system is used to measure errors. Each graph element in Figure 13 shows the results of the applied torque repeatedly applied for 50 times. The graph means that with the application of the same torque, the frequency of equal output voltage can be detected. For the maximum span ΔR of 0.07 V, the repeatability can be calculated as (21). max The graph presents the detected frequency of equal output voltage applying the same torque. ΔR max γ = × 100% = 2 32% 21 FS Photointerrupter-B 4.5. Factor of Safety. Generally, that the most effective Figure 8: Manufactured torque sensor. method to evaluate the property of factor of safety is to conduct the experiment of overload. The experiment is conducted with 0.5 Nm increment of load from 1 Nm to 5 Nm. In each load, the experiment is conducted about 3 where ΔL is the maximum error, FS is the full scale, ΔX is max times with maintaining load at least 5 minutes. After the full range of torque input change, and ΔY is the corre- removing the load, the output voltage of photointerrupter sponding change in the output voltage. is recorded in Table 7. From the results, we can clearly find that in the range of 1 Nm to 4.5 Nm, this sensor could operate normally, while at the torque size of 5 Nm, it has 4.3. Hysteresis. Hysteresis describes the degree of misalign- been failed. Therefore, the factor of safety of this sensor ment between the input and output with the forward and should be about 4.5. backward loads. The hysteresis experiment was tested by applying torque in ascending and descending manners at 4.6. Evaluation. The performance of the designed torque 0.098 Nm. The results of the hysteresis experiment are shown sensor is shown in Table 8. Recently, the research of flex- in Table 6 and Figure 12. The graph of the hysteresis curve ible spring applied to the torque sensor is less. Obviously, was drawn using MATLAB. With a maximum offset ΔH max the linearity is a little insufficient which may be caused of 0.006 V, the hysteresis is calculated as by its principle of sensing element or the especially flex- ure spring. However, compared with other optical torque ΔH max sensors [12–14], the torque sensor designed in this paper γ = × 100% = 0 2% 20 FS has a wide measure range and a small diameter, while Deformation (deg) Deformation (deg) Applied Bionics and Biomechanics 11 Oscilloscope Designed torque sensor Weights Stability voltage support Commercial torque sensor Test system Figure 9: Calibrate test system. U 120 0.5 1 1.5 2 Distance (mm) (a) (b) Figure 10: Experiment circuit: (a) working principle of photointerrupter; (b) measure range. Table 5: Experiment data. Torque (Nm) Minimum (V) Maximum (V) Average (V) Calculate (V) Error % error 0 4.40 4.43 4.4118 4.3250 −0.0868 2.87 0.098 4.05 4.12 4.0800 4.0231 −0.0569 1.88 0.196 3.70 3.75 3.7190 3.7211 0.0021 0.70 0.294 3.35 3.40 3.3730 3.4191 0.0461 1.53 0.392 3.04 3.08 3.0586 3.1171 0.0585 1.94 0.49 2.73 2.77 2.7496 2.8151 0.0655 2.17 0.588 2.43 2.47 2.4494 2.5131 0.0637 2.11 0.686 2.15 2.19 2.1654 2.2112 0.0458 1.52 0.784 1.89 1.92 1.8998 1.9092 0.0094 0.31 0.882 1.64 1.67 1.6560 1.6072 −0.0488 1.62 0.98 1.39 1.42 1.4038 1.3052 −0.0986 3.27 Photointerrupter-A Channel-A Channel-B Photointerrupter-B Relative collector current (%) d 12 Applied Bionics and Biomechanics 4.5 0.08 0.06 0.04 3.5 0.02 −0.02 2.5 −0.04 −0.06 1.5 −0.08 1 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Torque (Nm) Torque (Nm) Error Experiment data Ideal Fitted curve (a) (b) Figure 11: Experiment results of applied torque and resulting output: (a) linearity; (b) error. Table 6: Results of hysteresis. 4.5 Torque (Nm) Forward (V) Backward (V) Error (V) 0 4.410 4.407 0.003 3.5 0.098 4.079 4.079 0.000 0.196 3.717 3.717 0.000 0.294 3.372 3.370 0.002 0.392 3.060 3.054 0.006 2.5 0.49 2.746 2.746 0.000 0.588 2.446 2.441 0.005 2 0.686 2.160 2.160 0.000 1.5 0.784 1.894 1.892 0.002 0.882 1.650 1.649 0.001 0.98 1.398 1.398 0.000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Torque (Nm) Forward Backward the thickness of only 4 mm is the best of them. At the Figure 12: Hysteresis curve. same time, it is equally satisfied with a light mass and a high safety factor; hence, it has a compact and smart structure that can be perfectly applied to biomimetic robot joints. sensor is very small for being used in a biomimetic joint with a maximum output torque size of 1 Nm obviously. The linearity, sensitivity, repeatability, and hysteresis are 5. Conclusion 4.31%, 2.06 V/Nm, 2.67%, and 0.2%, respectively. In the future, using signal process to promote its performance In this paper, a highly reliable optical torque sensor is devel- oped for biomimetic robot joints in extreme embedded appli- and studying multiforce/moment condition with similar size are worth considering. Improving the measurement cations. To ensure the high reliability, the structure is designed based on a flexure spring, which is most commonly dimension of the torque sensor and its application capac- used in many fields. The thickness is reduced to 4 mm, the ity in the new generation of biomimetic robot joints are our next vision and priorities. weight is 16 g, and the factor of safety is 4.5. The torque Output voltage (V) Output voltage (V) Output voltage (V) Applied Bionics and Biomechanics 13 22 15 20 14 18 13 16 12 14 11 12 10 10 9 8 8 6 7 4 6 2 3.04 3.045 3.05 3.055 3.06 3.065 3.07 2.43 2.435 2.44 2.445 2.45 2.455 2.46 2.465 2.47 2.475 3.7 3.705 3.71 3.715 3.72 3.725 3.73 3.735 3.74 3.745 3.75 Output voltage (V) Output voltage (V) Output voltage (V) (a) (b) (c) 18 18 16 17 14 16 12 15 10 14 8 13 6 12 4 11 2 10 0 9 1.875 1.88 1.885 1.89 1.895 1.9 1.905 1.91 1.915 1.92 1.38 1.385 1.39 1.395 1.4 1.405 1.41 1.415 1.42 1.425 Output voltage (V) Output voltage (V) (d) (e) Figure 13: Repeatability curve: (a) torque 0.196 Nm; (b) torque 0.392 Nm; (c) torque 0.588 Nm; (d) torque 0.784 Nm; (e) torque 0. 98 Nm. Foundation for National Defense Science and Technology Table 7: Data of overload experiment. of Chinese Academy of Sciences (CXJJ-17-M109). Torque (Nm) 1 1.5 2 2.5 3.0 3.5 4 4.5 5 1 (V) 4.41 4.40 4.40 4.41 4.42 4.41 4.40 4.42 4.41 References 2 (V) 4.41 4.42 4.39 4.40 4.42 4.40 4.41 4.42 4.35 3 (V) 4.40 4.40 4.39 4.41 4.42 4.40 4.41 4.41 4.21 [1] D. Tsetserukou, N. Kawakami, and S. Tachi, “Design, control and evaluation of a whole-sensitive robot arm for physical human-robot interaction,” International Journal of Humanoid Robotics, vol. 6, no. 4, pp. 699–725, 2009. Table 8: Performances of designed torque sensor. [2] V. A. Ho, D. V. Dao, S. Sugiyama, and S. Hirai, “Development Item Optical torque sensor and analysis of a sliding tactile soft fingertip embedded with a microforce/moment sensor,” IEEE Transactions on Robotics, Mass 16 g vol. 27, no. 3, pp. 411–424, 2011. Diameter 60 mm [3] Q. Liang, D. Zhang, Y. Ge, and Q. 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A Highly Reliable Embedded Optical Torque Sensor Based on Flexure Spring

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Hindawi Publishing Corporation
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Copyright © 2018 Yuwang Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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1176-2322
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1754-2103
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10.1155/2018/4362749
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Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 4362749, 14 pages https://doi.org/10.1155/2018/4362749 Research Article A Highly Reliable Embedded Optical Torque Sensor Based on Flexure Spring 1 2 3 1 3 Yuwang Liu , Tian Tian, Jibiao Chen , Fuhua Wang, and Defu Zhang State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, China Department of Mechanical Engineering, Shenyang Ligong University, Shenyang, China Department of Mechanical Engineering, Northeastern University, Shenyang, China Correspondence should be addressed to Yuwang Liu; liuyuwang@sia.cn Received 23 October 2017; Revised 2 January 2018; Accepted 28 January 2018; Published 15 April 2018 Academic Editor: QingSong He Copyright © 2018 Yuwang Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We propose a new highly reliable and lightweight embedded optical torque sensor for biomimetic robot arm enabling the torque measurement in joints, which can measure torque of the joint by detecting torsion of its elastic element (mechanical structure or flexure element). Flexure spring is introduced as the elastic element of the torque sensor in this paper. Because of its curve modeling, flexure spring is not inclined to be broken contrast to crossbeam structure, which is commonly used in torque sensor. Thanks to this structure, we can build a torque sensor as an extremely compact and highly reliable size. Six types of flexure spring are proposed to be used as the elastic element of the torque sensor in this paper, which have the potential for the requirements of measurement range and multidimensional detection. The optical electronic, less influenced by electromagnetic interferences, is selected to measure the torsion displacement of the flexure spring. The proposed design is analyzed, which can obtain the successful measurement of the torque with a load capacity of 1 Nm. One of the designed optical torque sensors is optimized by FEM. The calibration and experiment are conducted to ensure its feasibility and performance. 1. Introduction Kang et al. [4] designed a mechanically decoupled six- axis force/torque sensor. It is a crossbeam sensor, which use This paper focuses on the design of a new highly reliable and strain gauge technique to detect force/moment. The size of lightweight embedded optical torque sensor for biomimetic this sensor is small with thickness of 37 mm, and the robots in order to ensure accuracy and stability while perform- maximum torque detected by this sensor is 40 Nm. Also, ing practical tasks of physical interaction with unstructured Ma et al. [5] presented three kinds of compact torque sensors using strain gauge technique. The structure of these sensors is environment. Biomimetic robot arm is used to realize dexter- ous taskssuch asinteractionwith human or manipulation with cartwheel flexure, which is also crossbeam. The measurement objects in hazardous conditions. To achieve the stability in ranges of these sensors are 7 Nm, 22 Nm, and 50 Nm, respec- contact with environment and realize safety while performing tively. The thickness is about 6 mm which is much suitable for tasks of physical interaction with human and unstructured using an embedded application. However, it is difficult to environment, it is essential to calculate the torque of each joint attach the strain gauge to the structure reliably while develop- of the robot arm. The torque information of the torque sensor ing the type of torque sensor which is commonly sensitive to greatly enhances the force perception ability of biomimetic electrical noise and temperature. Kim et al. [7] designed a robot joint. The development of embedded torque sensor, six-axis force/moment capacitive sensor using dielectric especially, a lightweight and highly reliable one, has been of elastomer. Its deformation results in variation of capaci- great interest for decades [1–3]. Based on its measurement tance, which is used for sensing force/moment. The size methods, the torque sensor can be classified as strain gauges of this sensor is 67 mm × 30 mm, and the measurement [4–6], capacitive [7–9], piezoelectric [10, 11], photoelectric range is 0.16 Nm. However, it is generally nonlinearity. [1, 12–17], and so on [18, 19]. Liu et al. [10] designed a no-elastic six-axis force/moment 2 Applied Bionics and Biomechanics irregular-shaped objects and has flexible obstacle avoidance sensor using piezoelectric. The maximum torque detected by this sensor is as high as 250 Nm when the size is small performance. a i = 1~7 are under-actuated joint units in as 50 mm × 30 mm. However, piezoelectric sensor is gener- the robSSot. Each under-actuated joint unit is made up of a ally too stiff for this condition. scissor mechanism, an elastic device, bottom links, and sup- Recently, lots of researchers have been interested in this port links. The robot is directly driven by a single motor. type of optical for its compact size, noncontact approach, Therefore, the output torque of the driving motor has a great and less electromagnetic interference. Kim et al. [12] influence on the holding stability of the robot. In Figure 1, (a) designed a three-axis force/moment optical sensor using is the torque sensor and (b) is the driving motor. The crossbeam which has a thickness of 7 mm and a diameter of inner ring of the sensor is fixed with the driving motor, 28 mm making it the most compact. Also, Shams et al. [13] and the outer ring is fixedly connected with the robot. presented an optical crossbeam torque sensor. This sensor The torque sensor we designed can accurately measure is compact with a thickness of 11 mm and a diameter of the output torque of the motor. Therefore, the torque sen- 80 mm. Tsetserukou et al. [14] proposed three types of opti- sor can be well applied to a biomimetic actuation similar cal torque sensors. The first one is the cross-shaped spring to the elephant’s trunk robot and is of great significance with a diameter and thickness of 30 mm which can be used for studying the stability and performance characteristics to detect 1.75 Nm load. The second one is the hub spoke- of a bionic robot system. shaped spring with a diameter of 42 mm and thickness of Six types of flexure spring are proposed to be used as the 6.5 mm, and the sensor can be used to measure torque up mechanical structure. And the proper optical electronic is to 0.8 Nm. The third one is the ring-shaped spring with a selected to measure the torsion of the flexure spring. As a diameter of 42 mm and thickness of 10 mm, which can be result, six typical torque sensors are designed in Section 2. used to handle torque up to 0.8 Nm. Simulations of all the six types of torque sensor were done Relatively speaking, the optical torque sensors tend to by FEM (finite element method) software ANSYS, which acquire much more deformation which is very suitable to are described in Section 3. Simulation results show that build a biomimetic robot. However, the proposed sensors 2-rib torque sensor under 1 Nm load covers the measure- are commonly close to the yield stress at the maximum of ment range of the selected optical electronic perfectly. torque size in which the overload protection needs to be The 2-rib torque sensor is selected to be further studied. added to keep it operating. However, it is inconvenient to And topology optimization of this sensor is represented build a sensor with this mechanism as it will increase the joint in Section 3. The 2-rib optical torque sensor is calibrated, size. Factor of safety is a property to evaluate the ability of and several experiments (linearity, hysteresis, and repeat- resistance to overload. It suggests the property of reliability, ability) are conducted in Section 4. which is equal to the yield stress divided by the allowed one. However, an ideal compact size of the structure with a high 2. Sensor Design factor of safety especially for the embedded sensor is very Torque sensor can be divided into two main parts, elastic ele- hard to acquire. The fact is that the factor of safety of optical ment and sensing element. Elastic element produces torsion torque sensors is generally limited to 1.0~2.0 [1, 14, 15, 34]. under the load of torque. The deformation accuracy is Flexure spring, also called planer spring or torsion spring, detected and measured by the sensing element (Figure 2). has been used in many fields for its advantages of compact Thus, the applied torque could be acquired by establishing structure and highly reliable performance [20–25]. It has the relationship between the torque and the torsion. been used to design a strain gauge sensor [22, 23]. However, the application of flexure spring to torque sensor has not 2.1. Sensing Element Design. As the input of torque sensor is been developed yet. In addition, limited to the mount space, usually connected to motor [26, 27], the optical technique there is also a challenge to build an optical torque sensor less influenced by electrical noise is preferred. In many types based on the spring. of optical detection, we decided to use ultrasmall size of In this paper, we develop a highly reliable embedded photointerrupter as sensitive element to measure the rela- optical torque sensor using flexure spring. The size of the tor- tive motion of sensor’s component. In those products, que sensor is designed to be extremely small, according to RPI-131 and RPI-121 are considered as their wide mea- that of joint with the output of 1 Nm. The flexure spring, with surement range and small size. Although its size is slightly the ability of storing energy and reducing the potential of large, we finally selected RPI-131 to obtain a wide mea- stress concentration, is applied to realize the high reliability surement range. The dimension of selected photointerrup- of torque sensor. In [33], we imitate an elephant’s trunk with ter is 4.2 mm × 4.2 mm × 5.2 mm, the measurement range is the special function of holding objects and propose a new about 0.6 mm, and its weight is only 0.05 g. type of shape-adaptive elephant’s trunk robot to which the embedded optical torque sensor could be well applied. As 2.2. Elastic Element Design. The performance of elastic ele- shown in Figure 1, the elephant’s trunk robot could be seen ment widely varies according to its material and configuration. as a biomimetic elephant’s trunk, whose effect could be equivalent to a kind of large artificial muscle. The robot 2.2.1. Material. Steel, aluminum, and titanium are general consists of a base and some under-actuated joint units; the materials used in the design of torque sensor. Although the size of which is very similar to the real trunk. In an unstruc- yield stress of aluminum is the smallest, we select it because tured environment, the robot can adaptively grab various its density is half of steel and 2/3 of titanium. Also, aluminum Applied Bionics and Biomechanics 3 (a) (b) Figure 1: Elephant’s trunk robot and torque sensor. (a) Elephant’s trunk robot; (b) application of torque sensor in biomimetic actuation. Elastic element Detection Torque deformed sensing application Torque size Establishment Signal acquiring relationship processing Figure 2: Working principle of torque sensor. is the most economical among these materials. As a result, the aluminum 7075 with yield of 500 MPa is selected to man- Table 1: Parameters of the torque sensor. ufacture the elastic element of torque sensor. Item Parameter Item Parameter Diameter 60 mm Mount 11 mm 2.2.2. Configuration. Two types of shapes, namely, axis struc- Thickness 4 mm Inner/outer flange ϕ 3 mm/ϕ 2.5 mm ture and crossbeam, are generally used in elastic element Hole 12 mm design. The axis structure is usually used to load big torque because of its highly reliable performance and its capability to reduce coupling [3, 14, 28, 29]. However, it is difficult to 4 Applied Bionics and Biomechanics be assembled into small space of a joint. On the other hand, The built physical model can be seen in Figure 3. the crossbeam is widely used because of its compact structure The work done in deflecting the sensor Δθ by torque T is and good linearity [1, 4, 5, 7, 12–16]. However, it tends to 1/2TΔθ, and for these parts, the stored energies due to produce stress concentration and even fail. torsion are U , U , and U . Therefore, 1 2 3 Flexure spring has been gradually applied in many fields such as cryocoolers [20, 21], sensors [22–24], and U = U + U + U = TΔθ 2 1 2 3 geophones [25] because of its compact structure and highly reliable performance. Contrast to the crossbeam, In this model, we accept the equivalent force F and this structure could be more flexible which is beneficial moment M stand for the applied torque T. They are to the requirement of the relatively wide deformation. In F = , this section, the elastic element design is configured based NR out on the flexure spring. M = FR − R , Because of the variety of the number and angle of ribs, the 0 out 1 configuration would have potential for different measure- where N denotes the number of ribs. For part I, we can ment ranges. Theoretically, the number of ribs could be calculate the normal force F and tangential force F as 11 12 any. However, one to six ribs are considered feasible. The F = F cos α , designed parameters of the torque sensor are mainly deter- 11 1 mined by the robot joint, whose maximum output torque is F = F sin α , 12 1 1 Nm. These parameters are shown in Table 1. And the six typical configurations are shown in Table 2. where α is the angle between F and horizontal. Therefore, the stresses are 2.3. Integration. The interrupter shield and bracket were F F xy M y 11 12 0 designed to vary the intensity of light and support the photo- σ = + + , 1x A I I interrupter, respectively. The interrupter shield is attached to σ =0, rib while bracket is attached to outer ring (shown in Table 2). 1y Obviously, we can find that the multirib configurations have 3 F 2y a wide measurement range and multidetection, while the sen- τ = 1 − , 1xy 2 A b sitivity is much lower. where A is the sectional area, which can be calculated as 3. Analysis A = b ⋅ h (h is the thickness and b is the wide). I is the moment of inertia, which is equal to b h/12. Due to In this section, the stiffness equations of the proposed con- figurations are deduced. With FEM simulation using the U = σεdV, 6 software of ANSYS, the theory is examined by building the relationship between design angle and stiffness. The optimal structures in these six typical configurations are where ε is the strain displacement. We can acquire the energy of part I as selected according to their analysis results. Through the opti- mization of topology also using ANSYS, we finally acquired 1 σ the ideal configuration. 1xy 1x U = σ ε dV = dV + dV 1 1 1 2 2E 2G 3.1. Physical Modeling. The stiffness k means the required F F xy M y 1 torque to produce a unit angle and can be calculated from 11 12 0 = + + dV A I I 2E k = T/Δθ = TR /Δs, 1 2 out 2 9 F 2y + 1 − dV 8 b GA where T is the applied torque, Δθ is the deformed revolving 2 2 3 2 2 2 F L F L M L F M L 3F L angle, R is the radius of out flange, and Δs is the produced 11 1 12 1 0 1 12 0 1 12 1 out = + + + + , tangential displacement. While T and R are given, the core 2EA 6EI 2EI 2EI 5GA out issue is to acquire the formula of torsion in these sensors. To complete it, several assumptions and simplified physical where E is the modulus of elasticity, G is the modulus of rigidity, L is the distance between point A and B x , y . model are needed. Assumptions 1 1 1 For part II, in any point P x , y of the ribs, it has (1) during the deformation, the cross section remains V = F cos α , initial conditions; N = F sin α , (2) for the selected Al-7075, the material of the beam is homogeneous; M = −F y − y + F x − x + M , P 11 12 2 1 1 2 1 (3) when the deformation is small, the calculation can be where V, N, and M are the tangential force, normal force, seen as linearly elastic. and moment size in point P, respectively. α is the angle 2 L Applied Bionics and Biomechanics 5 Table 2: Six typical configurations. Number of ribs 1 2 3 Shield Bracket Mount Photointerrupter Hole Diameter Configuration Rib2 Rib1 Inner flange Outer flange M , F , and F Multidetection M /F M , F z x y z x z x Number of ribs 4 5 6 Configuration M , F , and F M , F , and F M , F , and F Multidetection z x y z x y z x y L z Cross section M R (a) Part II P(x, y) F‵ 12 F x Part I Part III D C M 11 M 0 2 (b) (c) (d) Figure 3: Physical model of the torque sensor: (a) overall appearance; (b) part I; (c) part II; (d) part III. 6 Applied Bionics and Biomechanics Table 3: Results of finite element analysis. Ribs Structure Displacement Stress Results Max displacement 4.0835 deg Max stress 157.32 Mpa Max displacement 0.3097 deg Max stress 65.627 Mpa Max displacement 0.0272 deg Max stress 17.55 Mpa Max displacement 0.0134 deg Max stress 11.767 Mpa Max displacement 0.0074 deg Max stress 6.9949 Mpa Max displacement 0.0049 deg Max-stress 5.8602 Mpa 4.5 0.1 0.05 3.5 −0.05 2.5 −0.1 −0.15 1.5 −0.2 −0.25 0.5 0 −0.3 12 3 4 5 6 12 3456 Ribs Ribs Angle from equation Error Anglefrom FEM FEM (a) (b) Figure 4: Relationship between deformation and the number of ribs: (a) deformation; (b) error. Deformation (deg) Deformation (deg) Applied Bionics and Biomechanics 7 between F and V, which can be calculated as α = pi − θ − α . 2 1 A: Shape optimization is the moment in point B, which is equal to M + F L . Figure 1 0 12 1 Type: shape finder As the rib is the curve beam, the expression according to Unit: t the method of energy is given in [30] Time: 0 2014/9/23 15:57 2 2 2 M kV R N R M N P P U = dθ + dθ + dθ − dθ 9 2AEe 2AG 2AE AE Max or Min U = U + U + U + U , 10 2 21 22 23 24 where k is a factor depending on the form of the cross section (for regular section which is equal to 1.2), e is the distance from the centroidal axis to the neutral axis, e = R − b/ ln R + b/2 − ln R − b/2 , and θ is the angle from axis of x to point P. Therefore, we can separately cal- Remove culate the energy of U i =1,2, 3,4 as 2i Marginal M 1 2 Keep U = dθ = −F y − y + F x − x + M dθ, 21 11 2 1 12 2 1 1 2AEe 2AEe 2 2 Figure 5: Result of optimization. kV R kF R U = dθ = cos θ + α dθ, 22 1 2AG 2AG where M is the moment in point C, which is equal to F R 2 2 2 12 N R F R U = dθ = sin θ + α dθ, cos α − cos θ − F R sin θ − sin α + M . θ is the angle 23 1 3 0 11 0 3 1 0 2AE 2AE of the rib. The energy of part III can be calculated as M N F U = − dθ = −F y − y + F x − x + M sin θ + α dθ, 24 11 2 1 12 2 1 1 1 AE AE 3xy U = σ ε dV + dV 11 3 3 3 2 2G F F xy M y 1 9 F 31 32 2 where the coordinates of point B x , y and point 1 = − + dV + A I I 2E 4 GA P x , y are 2 2 2y x = −R cos α , 1 3 1 − dV y = R sin α , 1 3 2 2 3 2 2 2 F L F L F M L M L 3F L 31 2 32 2 32 2 2 2 2 32 2 = − − + + x = −R cos θ, 2EA 6EI 2EI 2EI 5GA y = R sin θ 15 Therefore, we can find the Δθ as For part III, we can calculate the normal force F and tangential force F as 32 2 U + U + U 1 2 3 Δθ = 16 F = F sin α , 31 4 And the stiffness can be obtained as F = F cos α , 32 4 k = 17 Δθ According to these formulations, we could make the where α is the angle between F and horizontal in this part, which can be calculated as α = α + θ − pi. Therefore, the conclusion that the stiffness of k is in proportion to the 4 1 0 ribs number of N, modulus elasticity of E, and thickness stresses in this part are of h. F F xy M y 31 32 2 + , σ = − 3x 3.2. FEM Static. The six typical configurations are analyzed A I I by using ANSYS. In the analysis, the mesh type is hexahe- σ =0, 3y dron element, and each model comprises approximately 35,000 elements and 140,000 nodes. A fixed constraint is 3 F 2y τ = 1 − , applied to the inner flange, and a torque load of 1 Nm is 3xy 2 A b applied to the outer flange. The analysis results are listed in 8 Applied Bionics and Biomechanics 0.14959 max 0.00133 max B: static structural B: static structural Figure Figure 0.13297 0.0011822 Type: equivalent elastic strain z M Type: total deformation Unit: mm/mm Unit: mm Time: 1 Time: 1 0.11635 0.0010344 2015-11-19 19:59 2015-11-19 19:59 0.099725 0.099725 Max 0.00088667 0.083105 Min 0.00059111 0.066484 Min 0.00044334 0.049863 0.00029556 0.033242 0.00014778 0.016621 Max 2.2587e − 9 min 0 min (a) (b) 91.759 max 15 max B: static structural Figure B: static structural Type: equivalent (von Mises) stress M 81.564 z Figure Unit: MPa Type: safety factor Time: 1 71.368 Time: 1 2015-11-19 19:59 10 2015-11-19 19:59 61.173 Min Max 50.978 Max 5.449 min 40.782 Min 30.587 20.391 10.196 0.00013769 min (c) (d) 0.12997 max 46.978 max C: static structural C: static structural Figure Figure 0.11553 41.758 Type: total deformation Type: Equivalent (von Mises) stress Unit: mm Unit: MPa x Time: 1 Time: 1 0.10109 36.538 2015-9-29 16:10 2015-9-29 16:10 0.086648 31.318 0.072207 26.099 Min 0.057765 20.879 Min 0.043324 15.659 Max 0.028883 10.439 Max 0.014441 5.2197 0 min 3.681e − 6 min (e) (f) Figure 6: FEA results of optimized structure: (a) deformation from M ; (b) strain from M ; (c) stress from M ; (d) factor of safety from M ; z z z z (e) deformation from F ; (f) stress from F . x x Table 3. The relationship of displacement with those 6 when the number of ribs increased. The maximum stress configurations as FEM and formulae is shown in Figure 4. of 157.23 MPa was less than the material yield stress of The displacement of the applied torque of the elastic 500 MPa. Therefore, in this condition, the stress was not element was reduced from 2.1381 mm to 0.0025852 mm the core issue to consider. Finally, the 2-rib structure Applied Bionics and Biomechanics 9 was found to be optimal because the deformation of one Table 4: Comparison of performances of original and optimized structure. rib was beyond the measurement range of RPI-131, while the deformation of others was significantly small. Furthermore, Item Original Optimized the displacement of 0.1627 mm was detectable using the 34,000 elements, 60,000 elements, RPI-131. Mesh 136,000 nodes 11,000 nodes Displacement 0.16086 mm 0.14959 mm 3.3. FEM Optimization. Optimization was measured to deter- Max stress 64.567 MPa 91.759 MPa mine the optimal structure. The topology optimization to Max strain 0.00089679 mm 0.00133 mm achieve the lightest weight was conducted using ANSYS with the reliability constraints and stress limitations. An efficient Factor of safety 7.7439 5.449 method for topology optimization is reducing the quality Mass 15.442 g 13.72 g and volume to make the model approach the optimized tar- get. In this case, the mechanical performance should be partly retained. In the analysis, the solid element was accepted. Approxi- 4.1. Experiment Preparation. The sensor, discussed in this mately 90,000 elements and 160,000 nodes were produced in paper, is manufactured with a computer numerical control the meshing. Similarly, a fixed constraint was applied to the milling machine (Figure 8), and the test system (Figure 9) is inner flange, and the torque was loaded at the outer flange. built to study its performances. Figure 10 shows the estab- The quality of the target optimization was set to half. lished experiment circuit. The photointerrupter is composed Figure 5 shows that the red area could be removed without of an infrared light emitting diode (LED) at one side and a significantly affecting the performance in mechanics. transistor (detector) at the other side (shown in Based on the result of optimization, we finally acquired Figure 10(a)). The graph in Figure 10(b) shows there is a the ideal configuration by modelling with the method of linear relationship between the distance and the current eccentric circle to approach the optimization results. To eval- of the collector. According to this linear relationship, uate the performance of the optimized 2-rib configuration, acquiring the applied torque size by detecting shield displace- the static analysis was reconducted. In the analysis, the solid ment would be successful. Considering the sensitivity, U = element was also accepted, and approximately 54,000 ele- 10 V and R =10 kΩ were selected [13]. R = 833Ω was cho- L 0 ments and 98,000 nodes were produced. The same torque sen for I ≈ U − U /R = 10V − 1 16 V /833Ω =10 4mA d 0 load and fixed constraint were applied on the outer and inner (where U ≈ 1 16 V that is the voltage drop caused by LED). flanges, respectively. As this sensor is immune to the loads of Channels A and B were linked to the oscilloscope channels 1 M , M , F , and F (the deformation from these loads could x y y z and 2, respectively. In this kind of circuit, the maximum out- not be detected by the photointerrupters), the influence by F put voltage was 9.8 V, and the output voltage in the initial posi- needs to be considered. In the analysis, the force load (15 N) tion was approximately 4.5 V. and fixed constraint were also applied on the outer and inner flanges, respectively. Figure 6 shows the analysis 4.2. Linearity. Linearity describes the degree offset between results of the optimized 2-rib structure. The comparison the actual line and ideal straight line [31, 32]. The torque of performances between the original and optimized struc- is achieved (from 0 Nm to 0.98 Nm) by placing load at the tures is listed in Table 4. lever of the test system, and the increased torque is According to (a) to (f) in Figure 6, we can obviously find 0.098 Nm. The experiment is conducted more than 50 that under the load of M , the deformations detected by the times to ensure the acquired data truly reflect the perfor- two photointerrupters are identical. While, under the load mance of the sensor. The experiment data are recorded of F , the deformations detected by the two photointer- in Table 5, and the graphs of linearity and error are drawn rupters are opposite. Therefore, the error caused by F , in Figure 11. With using polyfit function of MATLAB, the in a certain range, could be eliminated through the simple relationship between displacement and applied torque can signal process such as be average. Eventually, the designed be built as sensor could detect the torque of M without influence from other loads. Δ = −3 0198T +4 3250, 18 And through the topology optimization, the results show that the displacement was reduced by 7.01%, and the mass was reduced by 11.15%; meanwhile, the factor of safety was where Δ is the output voltage and T is the applied torque size. also reduced by 29.63%. Theoretically, the linearity of this The nonlinearity and torque sensitivity are expressed as sensor can be seen in Figure 7. ΔL 0 0986 max γ = × 100% = × 100% = 3 27%, 4. Experiments and Results FS 4 325 − 1 3052 ΔY 4 4118 − 1 4038 The performances of linearity, hysteresis, and repeatability S = = =3 07 V/Nm, ΔX 0 98 are important in evaluating the feasibility of the design of torque sensor. 10 Applied Bionics and Biomechanics −4 ×10 0.35 1.5 0.3 0.25 0.5 0.2 0.15 −0.5 0.1 −1 0.05 −1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Torque (Nm) Torque (Nm) Analysis results Error Fitted curve Ideal (a) (b) Figure 7: Simulation in the range of 0~1 Nm: (a) relationship of torque and displacement; (b) error. 4.4. Repeatability. Repeatability is usually necessary when Shield Photointerruper-A Flexure an unsteady system is used to measure errors. Each graph element in Figure 13 shows the results of the applied torque repeatedly applied for 50 times. The graph means that with the application of the same torque, the frequency of equal output voltage can be detected. For the maximum span ΔR of 0.07 V, the repeatability can be calculated as (21). max The graph presents the detected frequency of equal output voltage applying the same torque. ΔR max γ = × 100% = 2 32% 21 FS Photointerrupter-B 4.5. Factor of Safety. Generally, that the most effective Figure 8: Manufactured torque sensor. method to evaluate the property of factor of safety is to conduct the experiment of overload. The experiment is conducted with 0.5 Nm increment of load from 1 Nm to 5 Nm. In each load, the experiment is conducted about 3 where ΔL is the maximum error, FS is the full scale, ΔX is max times with maintaining load at least 5 minutes. After the full range of torque input change, and ΔY is the corre- removing the load, the output voltage of photointerrupter sponding change in the output voltage. is recorded in Table 7. From the results, we can clearly find that in the range of 1 Nm to 4.5 Nm, this sensor could operate normally, while at the torque size of 5 Nm, it has 4.3. Hysteresis. Hysteresis describes the degree of misalign- been failed. Therefore, the factor of safety of this sensor ment between the input and output with the forward and should be about 4.5. backward loads. The hysteresis experiment was tested by applying torque in ascending and descending manners at 4.6. Evaluation. The performance of the designed torque 0.098 Nm. The results of the hysteresis experiment are shown sensor is shown in Table 8. Recently, the research of flex- in Table 6 and Figure 12. The graph of the hysteresis curve ible spring applied to the torque sensor is less. Obviously, was drawn using MATLAB. With a maximum offset ΔH max the linearity is a little insufficient which may be caused of 0.006 V, the hysteresis is calculated as by its principle of sensing element or the especially flex- ure spring. However, compared with other optical torque ΔH max sensors [12–14], the torque sensor designed in this paper γ = × 100% = 0 2% 20 FS has a wide measure range and a small diameter, while Deformation (deg) Deformation (deg) Applied Bionics and Biomechanics 11 Oscilloscope Designed torque sensor Weights Stability voltage support Commercial torque sensor Test system Figure 9: Calibrate test system. U 120 0.5 1 1.5 2 Distance (mm) (a) (b) Figure 10: Experiment circuit: (a) working principle of photointerrupter; (b) measure range. Table 5: Experiment data. Torque (Nm) Minimum (V) Maximum (V) Average (V) Calculate (V) Error % error 0 4.40 4.43 4.4118 4.3250 −0.0868 2.87 0.098 4.05 4.12 4.0800 4.0231 −0.0569 1.88 0.196 3.70 3.75 3.7190 3.7211 0.0021 0.70 0.294 3.35 3.40 3.3730 3.4191 0.0461 1.53 0.392 3.04 3.08 3.0586 3.1171 0.0585 1.94 0.49 2.73 2.77 2.7496 2.8151 0.0655 2.17 0.588 2.43 2.47 2.4494 2.5131 0.0637 2.11 0.686 2.15 2.19 2.1654 2.2112 0.0458 1.52 0.784 1.89 1.92 1.8998 1.9092 0.0094 0.31 0.882 1.64 1.67 1.6560 1.6072 −0.0488 1.62 0.98 1.39 1.42 1.4038 1.3052 −0.0986 3.27 Photointerrupter-A Channel-A Channel-B Photointerrupter-B Relative collector current (%) d 12 Applied Bionics and Biomechanics 4.5 0.08 0.06 0.04 3.5 0.02 −0.02 2.5 −0.04 −0.06 1.5 −0.08 1 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Torque (Nm) Torque (Nm) Error Experiment data Ideal Fitted curve (a) (b) Figure 11: Experiment results of applied torque and resulting output: (a) linearity; (b) error. Table 6: Results of hysteresis. 4.5 Torque (Nm) Forward (V) Backward (V) Error (V) 0 4.410 4.407 0.003 3.5 0.098 4.079 4.079 0.000 0.196 3.717 3.717 0.000 0.294 3.372 3.370 0.002 0.392 3.060 3.054 0.006 2.5 0.49 2.746 2.746 0.000 0.588 2.446 2.441 0.005 2 0.686 2.160 2.160 0.000 1.5 0.784 1.894 1.892 0.002 0.882 1.650 1.649 0.001 0.98 1.398 1.398 0.000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Torque (Nm) Forward Backward the thickness of only 4 mm is the best of them. At the Figure 12: Hysteresis curve. same time, it is equally satisfied with a light mass and a high safety factor; hence, it has a compact and smart structure that can be perfectly applied to biomimetic robot joints. sensor is very small for being used in a biomimetic joint with a maximum output torque size of 1 Nm obviously. The linearity, sensitivity, repeatability, and hysteresis are 5. Conclusion 4.31%, 2.06 V/Nm, 2.67%, and 0.2%, respectively. In the future, using signal process to promote its performance In this paper, a highly reliable optical torque sensor is devel- oped for biomimetic robot joints in extreme embedded appli- and studying multiforce/moment condition with similar size are worth considering. Improving the measurement cations. To ensure the high reliability, the structure is designed based on a flexure spring, which is most commonly dimension of the torque sensor and its application capac- used in many fields. The thickness is reduced to 4 mm, the ity in the new generation of biomimetic robot joints are our next vision and priorities. weight is 16 g, and the factor of safety is 4.5. The torque Output voltage (V) Output voltage (V) Output voltage (V) Applied Bionics and Biomechanics 13 22 15 20 14 18 13 16 12 14 11 12 10 10 9 8 8 6 7 4 6 2 3.04 3.045 3.05 3.055 3.06 3.065 3.07 2.43 2.435 2.44 2.445 2.45 2.455 2.46 2.465 2.47 2.475 3.7 3.705 3.71 3.715 3.72 3.725 3.73 3.735 3.74 3.745 3.75 Output voltage (V) Output voltage (V) Output voltage (V) (a) (b) (c) 18 18 16 17 14 16 12 15 10 14 8 13 6 12 4 11 2 10 0 9 1.875 1.88 1.885 1.89 1.895 1.9 1.905 1.91 1.915 1.92 1.38 1.385 1.39 1.395 1.4 1.405 1.41 1.415 1.42 1.425 Output voltage (V) Output voltage (V) (d) (e) Figure 13: Repeatability curve: (a) torque 0.196 Nm; (b) torque 0.392 Nm; (c) torque 0.588 Nm; (d) torque 0.784 Nm; (e) torque 0. 98 Nm. Foundation for National Defense Science and Technology Table 7: Data of overload experiment. of Chinese Academy of Sciences (CXJJ-17-M109). Torque (Nm) 1 1.5 2 2.5 3.0 3.5 4 4.5 5 1 (V) 4.41 4.40 4.40 4.41 4.42 4.41 4.40 4.42 4.41 References 2 (V) 4.41 4.42 4.39 4.40 4.42 4.40 4.41 4.42 4.35 3 (V) 4.40 4.40 4.39 4.41 4.42 4.40 4.41 4.41 4.21 [1] D. Tsetserukou, N. Kawakami, and S. Tachi, “Design, control and evaluation of a whole-sensitive robot arm for physical human-robot interaction,” International Journal of Humanoid Robotics, vol. 6, no. 4, pp. 699–725, 2009. Table 8: Performances of designed torque sensor. [2] V. A. Ho, D. V. Dao, S. Sugiyama, and S. Hirai, “Development Item Optical torque sensor and analysis of a sliding tactile soft fingertip embedded with a microforce/moment sensor,” IEEE Transactions on Robotics, Mass 16 g vol. 27, no. 3, pp. 411–424, 2011. Diameter 60 mm [3] Q. Liang, D. Zhang, Y. Ge, and Q. 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