Abstract
Purpose
This study aims to propose a new variable stiffness robot joint (VSR-joint) for operating safely. More and more variable stiffness actuators are being designed and implemented because of their ability to minimize large forces due to shocks, to safely interact with the user and their ability to store and release energy in passive elastic elements.
Design/methodology/approach
The design of VSR-joint is compact and integrated highly and the operating is simply. The mechanics, the principle of operation and the model of the VSR-joint are proposed. The principle of operation of VSR-joint is based on a lever arm mechanism with a continuously regulated pivot point. The VSR-joint features a highly dynamic stiffness adjustment along with a mechanically programmable system behavior. This allows an easy adaption to a big variety of tasks.
Findings
Preliminary results are presented to demonstrate the fast stiffness regulation response and the wide range of stiffness achieved by the proposed VSR-joint design.
Originality/value
In this paper, a new variable stiffness joint is proposed through changing the cantilever arm to change the performance of the elastic element, which is compact, small size and simple adjustment.
Keywords
Citation
Tao, Y., Wang, T., Wang, Y., Guo, L., Xiong, H. and Xu, D. (2015), "A new variable stiffness robot joint", Industrial Robot, Vol. 42 No. 4, pp. 371-378. https://doi.org/10.1108/IR-11-2014-0422
Publisher
:Emerald Group Publishing Limited
Copyright © 2015, Emerald Group Publishing Limited
1. Introduction
The external environment is known in traditional commercial manufacture, so robot just relies on precise position control and moves along the designed route, finishing fairly repetitive tasks. Because these industrial robots are aiming at precise position control, rigid connections are used among different parts (Hongwen et al., 2009). However, when robot’s end-effector contacts with its surroundings, precise position control is not enough. If robot combines with contact force, the requirements for position precision will be released. Also, in this way, flexible variable stiffness connections used in robots will have important application value.
The elastic actuator is usually installed at robot’s joints, which provides a low-output damping friction to finish precise force control. Pratt and Williamson (1995) of MIT studied has elastic actuator since 1980s. Because elastic actuator possesses advantages that traditional driving modes do not have, many researchers start to study it. Researchers proposed different solutions afterwards. For example, Sensinger and Weir (2006) designed a rotary mechanism without backlash, Van Ham et al. (2009) designed a parallel mechanism, Sulzer et al. (2005) designed on sheave structure and Zhou et al. (2009) used damping link replaced elasticity. The basic theory of their designs is the same. For variable stiffness mechanism’s research, it is limited to rigid mechanism’s compliance control, while VICTORS, SMERobot and PHRIENDS were trying to develop a safety robot that can contact with people directly. VIACTORS proposed flexible variable stiffness mechanism like FS-Joint, VS-Joint, AWAS, VSA (Wolf et al., 2011; Catalano et al., 2011; Jafari et al., 2010; Kim and Song, 2010; Hung et al., 2011 Wolf and Hirzinger, 2008; Friedl et al., 2011) with a variable impedance system of dynamic performance, aiming at solving development and safety problems and saving energy.
Several types of VSMs can be realized by using different power transmission mechanisms, such as the variable effective length mechanism and the cam-follower mechanism. The mechanical impedance adjuster (Morita and Sugano, 1997), mechanically adjustable compliance and controllable equilibrium position actuator (Sensinger and Weir., 2006), actuator with adjustable stiffness I and II (Jafari et al., 2011) and variable stiffness joint (Kim and Song, 2010) are good examples based on this principle of operation. Recent research has focused on the use of tunable-stiffness materials, including field-activated materials like magnetorheological or electrorheological fluids (Visser et al., 2011; Choi et al., 2011). These technologies are promising for the precise control of damping, and are mostly used in active damping mechanisms such as tunable automotive suspensions. However, there are limitations in their achievable range of the elastic modulus, or yield strength, when they are activated. A hybrid dual actuator unit (HDAU) was proposed (Zhou et al., 2009). The HDAU was composed of a hybrid control module (HCM) based on an adjustable moment arm mechanism and a drive module with two motors. A hybrid variable stiffness actuator (HVSA) is proposed. The HVSA is a variable stiffness unit design based on an adjustable moment arm mechanism. The HVSA consists of an HCM and a drive module. In the HCM, a modified planetary gear train with a rack-and-pinion mechanism is adopted to exploit the adjustable moment arm mechanism. The HVSA controls both the position and the stiffness of the output shaft simultaneously, according to the angular positions of the ring gear and carrier. The HCM is connected to the drive module through gear trains so that the torque of each motor installed in the drive module is independently transmitted to the ring gear and carrier.
Most previous studies combine drive section with variable stiffness joint in the variable stiffness actuator (Tonietti et al., 2006; Koganezawa et al., 2006; Laffranchi et al., 2011; Hurst, 2004; Choi et al., 2008”), which on one hand makes the actuator compact and decreases the size of the whole drive joint in certain extent, and on the other hand the structure is complex and the reconfigurability is not enough to be used as a module in integrated applications.
In fact, when the size of variable stiffness actuator is close to the size of the joint of robot, such as medical rehabilitation service robot (Van Ham et al., 2009), it can have practical applications. So, it should be small sized with a wide range of stiffness, be able to adjust quickly and accurately, sensitive to the collision and safe to the human. In this paper, a new variable stiffness joint is proposed through changing the cantilever arm to change the performance of the elastic element, which is compact, small in size and simple adjustment.
The problems in traditional designs are solved such as large size, cumbersome stiffness adjustment mechanism, high requirements on the elastic element and the drive system caused by integrating the variable stiffness elements to drive section. Simultaneously, the relative rotation angle of the joint could be measured based on the encoder to achieve real-time control of the stiffness. In addition, real-time dynamic stiffness control of the joint can be achieved by adjusting the position of the slider even if the joint is working or has a load. The robot arm with the VSR-joint can be self-adaptive when the real-time closed-loop control system is set up. It tends to be more flexible to ensure safety and adjusts to be more rigid for the accuracy as well.
The paper is structured as follows. The design concept and working principle of the VSR-joint for adjusting the stiffness is presented in Section 2. The mathematical model of the VSR-joint is presented in Section 3. The simulation analysis and physical design is presented in Section 4. The conclusions and future works are proposed in Section 5.
2. Design of the variable stiffness robot joint
2.1 Design concept and working principle
The concept of the VSR-joint is based on the effective length of a variable leaf spring. The stiffness is changed by adjusting the position of the slider, which is connected to the leaf spring by a motor-driven ball screw. The ball screw is driven by the stiffness motor through a double reduction gearing. The rotation of the ball screw turns into the translation of the slider, leading the change of the effective length of the leaf spring. Thus, the stiffness of the VSR-joint is changed, as shown in Figure 1.
By the design concept above, the stiffness of the VSR-joint in such working principle is adjustable, as shown in Figure 2. The output terminal of joint motor cascades an adjustable springing, which can be adjusted by stiffness motor. Thus, the stiffness between the joint motor and the output link can be adjusted and observed.
2.2 Design of structure
The design of the VSR-joint is presented in this section. As shown in Figure 2, the joint is composed of two relative rotating disks, and the rotating center is in the middle of the joint. One side is the base of the VSR-joint, and the other is the rotator with a leaf spring as the buffer element. Each disk has mounting holes, through which connected to the joint motor or the link. The stiffness motor is fixed to the base and adjusts the position of the slider through the gear and ball screw. The leaf spring goes through the slider with its one side attached to the rectangular channel of the base and the other side inserted into the gap of the rotator.
Several rollers contained in the slider could roll on the surface of the spring to reduce friction between the slider and spring during adjustment. The spring is bent when a torque is applied to the joint base, which buffers the collision and stores the energy. The stiffness of the spring is determined by the material and the shape of the spring. Meanwhile, the stiffness of the joint is determined by the effective length of the spring, which can be controlled by the stiffness motor. When the slider moves to the fixed end of the spring, the effective length is increased, leading that the stiffness of the joint decrease. On the contrary, the stiffness of the joint is increased (Figure 3).
The spring steel is used in the VSR-joint, and the Young’s modulus is 200 GPa. The length of the spring is 100 mm. The thickness is 2 mm and the width is 8 mm. The effective length of the spring ranges from 10 to 70 mm, and the maximum of the angle of rotation is 9°. The dimensions of the VSR-joint are listed in Table I.
3. Model of the variable stiffness robot joint
The modeling of the VSR-joint is based on the schematic of the lever arm mechanism with leaf spring used in VSR-joint, as shown in Figure 4. When an external torque is applied to the base, the leaf spring is bent with a deflection angle Θ and a bending deflection ω. D is the diameter of the joint and L 0 is the length of the leaf spring. The effective length of the leaf spring is set as l and the force applied to the end of the leaf spring is set as F.
In this model, the deflection angleΘ: Equation 1
Then, the deflection of the leaf spring ω: Equation 2
E is the Young’s modulus of the leaf spring, b is the width of the leaf spring and h is the thickness of the leaf spring. Combining equations (1) and (2), the force of the end of the leaf spring is given as follows: Equation 3
Then, the torque of the joint is approximated as τ: Equation 4
Then, the stiffness of the VSR-joint formulated as k: Equation 5
The stiffness motor controls the position of the slider, and then changes the relative position of the pivot through the transmission the gear and screw. The effective length of the leaf spring is determined by the stiffness motor. In equation (6), s is the lead of the ball screw, i is the transmission ratio of the gear reducer and n is the rotation number of the stiffness motor: Equation 6
Combining equations (5) and (6), the stiffness of the joint is given as K: Equation 7
The stiffness of the VAR-joint is adjusted by controlling the stiffness motor. Because the designed deflection angle Θ is between ±9°, so c o s Θ trends to be 1. The main factor that influences the stiffness of the joint is the effective length of the leaf spring, and the influence of the deflection angle is ignored. This is clarified in Figure 4. So, the stiffness K is simplified as follows: Equation 8
The control complexity of the stiffness motor and the adjustment of the joint stiffness are reduced.
4. Simulation analysis and physical design
As defined in equation (7), the stiffness of the VSR-joint is adjusted by the effective length of the spring. With the effective length becoming longer, the stiffness is decreased and the allowable deflection angle is increased. The stiffness of the VSR-joint ranges from 10 to 800 Nm/rad, as shown in Figure 5. The torque changes when the pivot position moves from the end of the spring to the base. The maximum of allowable torque is shown in Figure 6 as the roller moving from the minimum to the maximum of the effective length of spring.
The physical internal and external design of the VSR-joint is shown in Figure 7. The main specifications of the VSR-joint analyzed in Section 3 are summarized in Table II (Figure 8).
5. The control strategy of the VSR-joint
The control of the VSR-joint contains the adjustment of the slider position, the collection of the deformation information and the information parsing of the joint stiffness mainly. According to the work target of the VSR-joint, the program flow chart is given, as shown in Figure 9.
The strategy of the position information calibration is shown in Figure 10. The high precision photoelectric encoder is presented to measure deformation between the joint base and the rotator. The slider position is tested by the motor encoder, which is incremental and must be calibrated. Considering the different load when the VSR-joint is power on, the zero position is defined at the centrifugal end.
The strategy of data parsing transforms the stiffness is set by upper computer to the information of slider position. Due to mechanical clearance, the positive and negative rotation of motor result in D-value. If the D-value is △d, the data parsing of the target location is P, as shown in Table III.
6. Experiment and performance of the system
6.1 Experimental platform
As shown in Figure 11, the experimental platform is set up to investigate the performance of the VSR-joint. The VSR-joint is attached to the horizontal steel frame, and an output link of length of 250 mm is connected to the output shaft of the VSR-joint. As the output link rotated in response to the external force, the joint torque of the VSR-joint is measured by the load and the arm of the output, and the deflection angle of the output link is simultaneously measured by the optical encoder in the VSR-joint.
6.2 Performance of the system
6.2.1 Stiffness control
As described in Section 3, the joint stiffness of the VSR-joint can be adjusted by controlling the effective length of the spring. The relationship between the output torque and the deflection angle is measured at every 5 mm interval in the boundary condition, as shown in Figure 12. The experimental results show that the joint torque of the VSR-joint was linearly proportional to the deflection angle under different stiffness.
The variation of joint stiffness for various effective length of the spring is shown in Figure 13. The theoretical joint stiffness was obtained through the equation (8). The measured joint stiffness shows good agreement with the theoretical joint stiffness. A small amount of hysteresis is observed when the external torque is applied or released. This problem is related to the friction between the internal parts of the VSR-joint.
Next, the step responses for stiffness variation are investigated for different loads and different stiffness values. It takes about 1.5 s from the minimum to the maximum stiffness under no load, and the response time increased to 2 s under a load of 2 N · m, as shown in Figure 14.
6.2.2 Position control
To investigate the performance of position control, the step responses for an amplitude of 20° are investigated for the minimum and maximum joint stiffness. As shown in Figure 15, the oscillatory response lasts about 2 s for the minimum joint stiffness, and disappears within 1 s for the maximum joint stiffness. Because there is a compliant element existing between the link and the motor which can store the elastic energy, the link velocity can be made higher than the motor speed in a specific region when the elastic energy is converted to kinetic energy.
We also conduct experiments on tracking a sinusoidal trajectory with the amplitude of 20° in different stiffness conditions. A 0.5 kg weight is installed at the end of output link to verify the positioning accuracy of the VSR-joint for loading condition. The VSR-joint is attached to the horizontal frame, so there was no effect of gravitational force, but the effect of inertial force due to the weight. The joint stiffness is set to 10.38, 24.42 and 78.46 N · m/rad; the elastic motion of the output shaft caused a series of deviations. However, the deviations are decreased as the joint stiffness is increased, as shown in Figure 16.
7. Conclusions and future works
A new variable stiffness robot joint is proposed, which is small enough to connect to the end of joint and the position and stiffness are adjustable. The characteristics of the VSR-joint are analyzed, and a series of experiments are given to investigate the variable stiffness range and the response time. Following are some conclusions:
The measured joint stiffness of the VSR-joint shows good agreement with the theoretical joint stiffness, and the joint torque of the VSR-joint is linearly proportional to the deflection angle under different stiffness.
The VSR-joint is capable of variable stiffness in the range of 10.38-78.46 N · m/rad. The response time required for stiffness variation is about 2 s under a load of 2 N · m.
As the joint stiffness is increased to the maximum, the oscillatory response disappears within 1 s, and the deviations decrease to reasonable value on tracking a sinusoidal trajectory.
The size of the VSR-joint is very small, compared to other variable stiffness actuator abroad. This increases its practical applications greatly.
After doing experiments, we find some problems on the VSR-joint. The internal mechanical structure of hinder the slider, leading that we could not adjust the effective length of the spring smaller. Thus, the range of stiffness adjustment could not reach 800 N · m/rad, which is smaller than the pre-designed. There are friction and interspaces between the internal parts of the VSR-joint, which affects the performance of the VSR-joint.
In the next version, we will improve and optimize the performance of the VSR-joint. Then, we will conduct experiments on mechanical arm with a dynamically adjustable stiffness, which contains three to five joint motors and the VSR-joints to investigate the safety of the mechanical arm when interacting with human in the uncertain environment.
Figure 1
The schematic of the VSR-joint stiffness is based on the leaf spring with rollers. When the rollers slide on the leaf spring, the effective length of the spring changes, which is the distance between the rollers and the rotator. With small reduction in the effective length of the spring, the stiffness of the VSR-joint increases
Corresponding author
Yong Tao can be contacted at: [email protected]
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Further reading
Howard, M. , Braun, D.J. and Vijayakumar, S. (2013), “Transferring human impedance behavior to heterogeneous variable impedance actuators”, IEEE Transactions on Robotics , Vol. 29 No. 4, pp. 847-861.
Kim, B.S. and Song, J.B. (2012), “Design and control of a variable stiffness actuator based on adjustable moment arm”, IEEE Transacitons on Robotics , Vol. 28 No. 5, pp. 1145-1151.
Kim, Y. , Cheng, S. , Kim, S. and Iagnemma, K. (2014), “A stiffness-adjustable hyperredundant manipulator using a variable neutral-line mechanism for minimally invasive surgery”, IEEE Transactions on Robotics , Vol. 30 No. 2, pp. 382-394.
Mancini, M. , Grioli, G. , Catalano, M., , Garabini, M. , Bonomo, F. and Bicchi, A. (2012), “Passive impedance control of a multi-DOF VSA-CubeBot manipulator”, IEEE International Conference on Robotics and Automation, IEEE, St. Paul, MN, pp. 3335-3340.
Vanderborght, B. , Tsagarakis, N.G. , Semini, C. , Van Ham, R. and Caldwell, D.G. (2009), “MACCEPA 2.0: adjustable compliant actuator withstiffening characteristic for energy efficient hopping”, in IEEE International Conference on Robotics and Automation , IEEE, Kobe, pp. 544-549.
Acknowledgements
This work was supported by the Youth Science Fund Project NO.61305116of the National Natural Science Foundation.