Towards Scalable Strain Gauge-Based Joint Torque Sensors

During recent decades, strain gauge-based joint torque sensors have been commonly used to provide high-fidelity torque measurements in robotics. Although measurement of joint torque/force is often required in engineering research and development, the gluing and wiring of strain gauges used as torque sensors pose difficulties during integration within the restricted space available in small joints. The problem is compounded by the need for a scalable geometric design to measure joint torque. In this communication, we describe a novel design of a strain gauge-based mono-axial torque sensor referred to as square-cut torque sensor (SCTS), the significant features of which are high degree of linearity, symmetry, and high scalability in terms of both size and measuring range. Most importantly, SCTS provides easy access for gluing and wiring of the strain gauges on sensor surface despite the limited available space. We demonstrated that the SCTS was better in terms of symmetry (clockwise and counterclockwise rotation) and more linear. These capabilities have been shown through finite element modeling (ANSYS) confirmed by observed data obtained by load testing experiments. The high performance of SCTS was confirmed by studies involving changes in size, material and/or wings width and thickness. Finally, we demonstrated that the SCTS can be successfully implementation inside the hip joints of miniaturized hydraulically actuated quadruped robot-MiniHyQ. This communication is based on work presented at the 18th International Conference on Climbing and Walking Robots (CLAWAR).


Introduction
In this paper, we focused on strain gauges-based joint torque sensors with the aim of exploiting their mechanical robustness [1] and scalability. It is based on work presented at the 18th International Conference CLAWAR [2]. Despite decades of reported studies on various strain gauges-based sensors for measuring joint torque over the years [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], their basic design has not improved significantly and most have restricted applicability in view of the strict requirements regarding linearity and symmetrical behavior to cope with different scales [20] necessitated by specific applications. The reason for this issue is well reported in literature, which clearly documented a trade-off between two factors i.e., sensitivity and torsional stiffness. The torsional stiffness is sacrificed at the expense of sensitivity, and vice versa. There is a third consideration that affects the design of a torque sensor. This relates to the means for securing fixation of the strain gauges on the torque sensor as this has an impact on both the shape and achievable performance.  [3,4,26]; (b) hub-sprocket four spokes [5,6,[27][28][29][30]; (c) hub-sprocket two spokes; (d) hub-sprocket with 4-bar linkage [9]; (e) hollow hexaform [31]; (f) new proposed design of Square-Cut Torque Sensor(SCTS), proposed in this communication.

Torque Sensor Design
The SCTS is based on a novel square-cut design, which embodies all of the desired attributes needed for joint torque sensing, i.e., high degree of linearity, symmetry, scalability and easy mounting of strain gauges. The design parameters of the sensor geometry are shown and defined in Figure 3. The SCTS has two twin-wings that are stretched or compressed depending on the torque clockwise/counterclockwise rotation. The outer and inner diameter of the sensor (D 6 , D 2 , respectively) can be seen in Figure 3. The thickness and width of the two wings are labelled H and W, respectively, in the Figure 3 (Left,Center). The wings are curved, C, outlining a hollow cylindrical space to avoid unwanted buckling. The Parameters K 1 and D 4 define keyhole locking of sensor with the outer (driven) link. K 2 defines the symmetric separation distance between each side of the twin-wings. The strain-gauges are glued on to the respective outer surface of wings (encircled in red, Figure 3 (right)). They are electrically connected via half-bridge in order to maximize the signal and provide temperature compensation.  Figure 4) is started by considering a hollow shaft shape, and then adding an internal smaller hollow circular section, to be used as a connection for the motor axle, connected to the external one by means of four wings. This choice, as aforementioned, was abandoned because the wings were too flexible so that the higher strains were achieved on their surface that was smaller and uncomfortable for the strain gauges' gluing. Thus, two wings were cut while the section of the remaining two was increased in order to transfer the higher strain values on the external surface of the sensor. This one was designed flat to have a wider and comfortable surface for the strain gauges' gluing. The remaining surfaces were shaped instead in agreement with the requirement of the joint design. Torsion in solid shaft creates shearing stress τ, which varies directly as the distance 'r' from the axis of the shaft. The stress distribution in the plane of cross section can be seen in Figure 5 (left), which creates the complementary shearing stresses in an axial plane. The highest shear stress occurs on the surface of the shaft. When it is subjected to applied torque T, the stresses flow is given by τ = Tr I , where the radius r is maximum, I = πD e 4 32 is the second moment of area and D e is the section diameter. However, the SCTS geometry was achieved starting from considering the analytical solution of torsion in a hallow shaft having closed cross section with thin walls, as shown in Figure 5 (right).

SCTS geometry evolution (in
In the case of a hollow circular section, we have where D e and D i are the external and the internal diameter, respectively. As consequence, the strains are given by where L is the beam length and G is the shear modulus, which strictly depends on the material properties. As is it possible to notice in Equation (2), the strains' values depends directly from both the value of the torque applied and the beam length, while, inversely, they depend on the material properties and geometry. Both stresses and strains are higher on the external surface of the beam that, for these reasons, became eligible for gluing the strain gauges. We simplified SCTS analytical model by considering its single wing as it is highlighted in Figure 6a, where force F max was exerted by keyhole lock surface on SCTS (marked with red solid) and the second moment of inertia create a bending moment M at point A. Considering, SCTS's wing geometry for Point A to Point B in Figure 6b can be represented by simple rectangular beam in Figure 6c. The uniaxial normal strain at this wing can be calculated by using its dimensions, the moment of inertia and position of the neutral axis. According to beam theory, a bending moment M ( M = F × d, where F is defined as a function of applied Torque T and design variables (see Figure 3 2 ) at point A causes a uniaxial normal stress, σ x , given by Equation (3) where y is for distance from the neutral axis, SCTS's wing width W and thickness H. The uniaxial normal strain ε x on each wing can be predicted by where the elastic modulus, E, of the material. Due to complex geometry of SCTS, the final shape of SCTS is obtained by using finite element analysis (ANSYS simulation), and this is discussed in the next section.

Simulations and Analysis
Finite element analysis was used to obtain the final shape and to envisage the behavior of the torque sensors, and for sensitivity analysis with respect to four parameters: material, size, wing width W and thickness H. The simulations presented in this section demonstrate that it is possible to modify the performance of the torque sensor in terms of measurement scale and sensitivity without affecting its linearity and symmetry.
The SCTS structure, moreover, avoids residual differences between clockwise and counter-clockwise applied (due to machining, geometrical tolerances and material properties, etc.), thereby ensuring that the behavior remains symmetric, as shown in simulated strain in the Figures 7 and 8. The strain-gauges are placed at external flat surfaces, and this is indicated by a white outlined box at the upper and lower surfaces of left side wings. Another significant improvement resulting from the twin-wing design is that of empowering SCTS with exhibiting a linear behavior together with high strain because the wings are only stressed within minor displacements, ensuring linear strain [34], but it also facilitates attachment of the strain-gauges to the maximal strain point. In addition, the gluing site for the strain gauges was specifically located on the outer flat surface of SCTS, and this is shown by a white outlined box in Figure 8.

Numerical Model
Numerical simulations were performed to investigate the parameters influencing the torque sensor behavior, e.g., material used, scale, wing width and thickness. Table 1 summarizes the simulation plan and parameters investigated. All of the ratios in Table 1   The analysis showed that Titanium and Aluminium alloy behaved weakly when compared to the steel alloy 39NiCr3Mo due to their mechanical properties. The torque sensor scale ratios studied were 1:0.75 and 1:1.25, respectively. The wing width W and thickness H were each investigated using high and low ratios ( Table 1). All of the simulations were carried out with ANSYS r15 program (ANSYS, Inc., Canonsburg, PA, USA), using a quadratic element mesh with six degrees of freedom for each node, suitable both for linear and for nonlinear applications (SOLID 189, ANSYS user manual), shown in Figure 9. The constraint and the load applied reproduced the experimental tests conditions (see Section 5).
At the start of the simulation, the stress was checked to ensure that the torque sensor was well within the yield strength point for different materials, before the parameters were investigated. It can be seen in Figure 10 for the steel alloy 39NiCr3Mo. The following analysis indicated that SCTS exhibited a linear and symmetric behaviour, the details and recording of which are reported in the remainder of this section.

Effects of Material
Three materials were investigated to determine their effect on strain while considering fixed initial sizing of SCTS and maximum applied torque. The 7075 Aluminium (Ergal) was found to be very stressed when reaching the yield point at 25 Nm of torque and the stress on the titanium averaged 33 Nm, indicating that both materials were unsuitable for the intended load (60 Nm) for the same physical dimensions of SCTS. As shown in Figure 11, the only material with the strength to cope with the desired torque load is a steel alloy 39NiCrMo3 for the same physical dimensions of SCTS.  Figure 11) ratio. This is given by the torsional moment that generated flexural moment M = F × d on the wing ends (as shown in the Figure 6). There is a geometrical nonlinearity in the Equation (4), depending on and y that change with respect to the applied torque T, which causes strains in the Ergal that seem to be larger than steel [35,36].

Effects of Scaling
The overall size of the sensor varied incrementally (increased and decreased by 25%). The design parameters for this simulation are D 1 = 15 to 25 mm, D 2 = 19.5 to 33.5 mm, D 3 = 22.5 to 37.5 mm, D 4 = 24 to 40 mm, D 5 = 27 to 45 mm, D 6 = 30 to 50 mm, K 1 = 9 to 15 mm, K 2 = 11.25 to 18.75 mm, W = 11.25 to 18.75 mm and H = 3 to 5 mm. The results demonstrate that size has a significant direct relation on strain, the strain being doubled or halved, as shown in Figure 12.

Effects of Wing Width and Thickness
The variation in SCTS's wing width W and thickness H significantly influenced the strain rate. In particular, the increment of 1.25 of width is less sensitive than 1.25 of thickness, and this was expected according to the applied design rules [37], as shown in Figures 13 and 14. Relationship between the torque and the strain depending on the wing thickness parameter: the 25% of variation influences torque sensor behavior. The reduction increases more than 40% the strain and the increment of the thickness reduces it by 25%. This means that the width reduction has more influence than the width increment.

Effects of D
The selection of SCTS's inner shaft diameter D 1 and outer diameter D 6 is mainly constrained by the available joint space where SCTS need to be fitted. By fixing its outer diameter D 6 , the variation in SCTS's inner shaft D 1 can be seen in Figure 15. Once D 1 and D 6 are defined, then the rest of the design parameters follow them. However, the increment or decrement in K 1 and K 2 by 25% exhibits similar behavior and it can be seen in Figures 16 and 17.

Experimental Results
Based on FEM simulation data, SCTS was machined of the steel alloy 39NiCr3Mo. The half bridge strain gauges were easily glued on both sides of the sensor to maximize the signal and provide temperature compensation. An experimental test rig layout is shown in Figure 18, where the relevant end of beam is loaded with weight at fixed lever-arm b in order to apply clockwise/counter-clockwise torque on the SCTS. The experimental setup for testing the SCTS is shown in Figure 19, and the torque is generated from placing a weight on the beam end. The applied torque is defined as τ = m × g × b, where g is the gravity acceleration. It is varied by changing weight 'm' applied on beam. This torque sensor is designed measuring a maximum torque of 60 Nm. Its design parameters are D 1 = 20 mm, D 2 = 26 mm, D 3 = 30 mm, D 4 = 32 mm, D 5 = 36 mm, D 6 = 40 mm, K 1 = 12 mm, K 2 = 15 mm, W = 15 mm and H = 3 mm (see Figure 3). The safety factor for SCTS is 3.96, and it is computed using ANSYS simulation working stress results at intended load and material yield stress. Figure 19. This experimental setup hardware mainly consists of three parts i.e., the spline shaft, the SCTS and beam. The spline shaft is fixed on the table and torque sensor inner shell is locked on it with zero-mechanical play. The beam that is locked on outer key locks of sensor and load is applied at its end in order to generate the torque. The attachment screw is used for the extension of the beam to increase its lever arm b.
An in-house constructed signal processing board was used to amplify the output of SCTS analog signal and its conversion to 18-bit digital signal.

Validation
The experimental data are compared with the FEM simulation and analytical estimation data. It is shown in Figure 20 confirming the reliability of the SCTS design in terms of its linear and symmetric output. Obvious discrepancy between experimental and FEM results at the torque value of ± 30 Nm can be seen. It is due to the nonlinearity of the strain gauges and bonding glue under the strain gauges. Moreover, this small difference between the FEM simulation and direct experiments will be used for future refinements of the SCTS torque sensor to further enhance its accuracy and reliability. According to the calibration curve (it can be seen in Figure 21), the following SCTS measurement characteristics are determined [38,39]: sensitivity: 141.3 mV/Nm, offset: 6.7 mV, linearity: 0.23% of F.S, full scale: 60 Nm and accuracy: 0.5% and noise and signal to noise: 3.7%.

Conclusions
This paper presented details of a novel SCTS design that is easily customizable for compact joint torque measurements. SCTS was also successfully integrated into the hip joint of each miniaturized hydraulically actuated quadruped robot-MiniHyQ [33] leg, and it can be seen in Figure 22 (left). The MiniHyQ hip joint computer-aided design (CAD) is shown in Figure 22 (right), where the SCTS center is locked on the hydraulic rotary motor's spline shaft, and its outer keyholes are locked with a driven link. In this application, SCTS provides efficient and reliable hip joint torque sensing up to a maximum of 60 Nm. The novel joint torque sensor, apart from its simple design, exhibits linear and symmetric output coupled with high sensitivity in both clockwise and counter clockwise directions. These attributes are underpinned by the robust nature of the sensor structure, easy access for strain-gauge gluing/fixing and the half bridge electric connection. SCTS is instantaneously capable of reporting the amount of torque applied with a sensitivity of 141.3 mV/Nm. It meets a range of requirements depending on the intended applications. In practice, it is possible to modify torque sensor performance in terms of measurement range and sensitivity without adversely affecting its linearity and symmetry, simply by altering overall size, material type and/or wings width and thickness. The study showed reasonable correlation between simulation (FEM) predicted and observed experimental data. The initial un-strained bridge measurement (output signal) was accounted for to avoid restriction on the obtained resolution and nullified the offset of the initial voltage. We used 18-bit analogue-to-digital converter to provide 3.4 µV of resolution, which ensured the reading of the desired signal. However, the effects of design parameters on SCTS bandwidth and dynamic measurements, including the resolution at higher frequencies, will be reported in future work. Hence, future research is also envisaged to optimize the structure in order to improve strain rate. In these future studies, several design parameters will be explored as outlined in Figure 3. Additionally, the application of SCTS in different scale rotary joints will be evaluated.
Author Contributions: All authors have made significant contributions to the paper. H.K. conceived the idea and designed the experiments; M.D. and F.C. performed the finite element analysis simulations; D.G.C., A.C. and C.S. coordinated and supervised the research; H.K. F.C. and M.D. wrote and revised the paper. A.C. and C.S. improved and corrected the English of the paper.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript: