IROS2019国际学术会议论文集 2412

Single Motor based Bidirectional Twisted String Actuation With Variable Radius Pulleys Muhammad Arshad Khan1 Bhivraj Suthar1 Igor Gaponov2 Jee Hwan Ryu3 Abstract In this paper is proposed a variable radius pulley VRP to linearize input output behavior of twisted string actuators TSA With the help of a VRP it is possible to make the inherently nonlinear transmission ratio of twisted string constant This enables design of bidirectional transmis sion systems driven by a single motor much like is done in conventional belt transmissions Herein we analyze the limi tations on employing constant radius pulleys in bidirectional twisted string transmission systems and propose a VRP design methodology based on TSA kinematics We manufactured the pulley and evaluated its performance experimentally in a series of unidirectional and bidirectional actuations The experiments demonstrated that the resultant transmission ratio from motor to load remained nearly constant as expected from the simulation results Different statistical measures for error between the experimental and simulated results were also calculated Keywords TwistedString Tendon WireMechanism Compliant Joint Mechanism Variable Radius Pulley I INTRODUCTION The expanding use of robots in daily human lives goes hand in hand with the use of safer and simpler actuation methods to facilitate human robot interaction With this trend conventional rigid robotic systems are often replaced by compliant actuation systems that are safer to operate around humans and signifi cant progress has been made in this regard in both software and hardware In recent years several novel actuator technologies have been proposed that are quieter more effi cient and safer when it comes to interaction with the surrounding environment Among them twisted string actuators TSA have emerged as mechanically simple cheap and more effi cient alternatives to conven tional actuators Their inherent compliance and potential for variable stiffness make these actuators attractive for use in human robot interaction Manuscript received February 25 2019 Revised May 28 2019 Accepted June 22 2019 This paper was recommended for publication by Editor Paolo Rocco upon evaluation of the Associate Editor and Reviewers comments This research was partially supported by the project Toward the Next Generation of Robotic Humanitarian Assistance and Disaster Relief Fun damental Enabling Technologies 10069072 and by the National Re search Foundation of Korea NRF grant funded by the Korea government MSIP No NRF 2016R1E1A1A02921594 1School of Mechanical Engineering Korea University of Technology and Education 1600 Chungjeolno Cheonan Chungnam South Korea marshad bhivrajiitd koreatech ac kr 2Faculty ofComputerScienceandEngineering Innopolis University 1Universitetskayast Innopolis 420500Russia i gaponov innopolis ru 3Department of Civil and Environmental Engineering Korea Advanced Institute of Science and Technology 291 Daehak ro Yuseong gu Daejeon 34141 South Korea jhryu kaist ac kr Digital Object Identifi er DOI see top of this page The basic concept behind TSA operation is that twisting of a string attached co axially to a motor results in its shortening and generates high unidirectional pulling forces This simple actuation method has found its utility in many conventional and modern robotic applications like assistance devices 1 2 3 robotic hands 4 5 6 mobile robots and many others Although TSA has many advantages it is limited to being a unidirectional actuator because it can only apply pulling force In order to apply bidirectional force a pair of TSAs can be connected to the same object antagonistically which implies using two motors to contract cables in opposite directions to actuate the joint bidirectionally and to control its stiffness In several previous studies antagonistic TSA confi gura tions were investigated in various robotic applications such as variable stiffness robotic joints as explored by Shisheie et al 1 Popov et al 7 G Palli et al 8 and Park et al 9 However using two motors for single joint actuation is not cost effective and the non linear nature of TSA contraction with twisting complicates control over antagonistic TSA based systems If not actuated properly these systems may suffer from increased string wear due to in fi ghting between them as well as from cable slack and loss of tracking accuracy as the result of it There was a trial to realize bidirectional TSA using only a single motor Mehmood 10 proposed using a yoke pin mechanism between the string and the controlled joint to linearize the string behavior The proposed mechanism had kinematic characteristics opposite to those of a TSA and thus serial connection of twisted strings to the mechanism resulted in a nearly linear relationship between the motor angle and pulley displacement Although this design enabled the use of a single motor to control a joint bidirectionally proposed system suffered from mechanical drawbacks such as rapid wear due to increased friction between the pin and pulley groove and required use of a linear mechanical guide which increased its weight and complexity Thus there remains a need for more effi cient linearization techniques for antagonistic joints controlled by TSA The main contribution of this paper is the design of a variable radius pulley VRP to linearize the input output behavior of a TSA With the proposed VRP we developed a bidirectional TSA driven by a single motor While VRPs have been previously used in series elastic actuators and pneumatic artifi cial muscles 11 12 to the best of our knowledge this study is the fi rst to address VRP design for TSA application We describe in detail the methods used to IEEE Robotics and Automation Letters RAL paper presented at the 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 Copyright 2019 IEEE design the pulley profi le depending on TSA parameters and then report the experimentally evaluated system performance in both uni and bidirectional actuation scenarios with a physical VRP The experiments demonstrate that the resulting VRP profi le helps cancel out the nonlinear transmission characteristics of the TSA resulting in a nearly constant transmission ratio II BIDIRECTIONALTWISTEDSTRINGACTUATION BY USINGA SINGLEMOTOR A Twisted String Kinematics In this section we discuss the general kinematic relation ships that describe twisted string behavior and outline the main problems of single motor based bidirectional twisted string actuation When a string is twisted it contracts and thus behaves as a rotary to linear transmission mechanism with a non linear transmission ratio 13 14 Assuming that the string with length L and radius r is twisted by angle and contracts by X amount the relationship between the angle of twisting and linear contraction can be described as follows X L p L2 2r2 1 Model 1 suggests that the relationship between the string s contraction X and angle of twisting is nonlinear and that the contraction rate increases with twisting We will refer to this model later when discussing joints driven by twisted strings that are installed antagonistically The transmission ratio KTSA of a TSA can be defi ned as the ratio between the motor angular velocity and the linear speed of string contraction Numerically the transmission ratio can be calculated using the ratio of the motor s angular and string s linear differential displacements Assuming these differential displacements to be and X corre spondingly one can fi nd the transmission ratio KTSA as follows KTSA X L2 r2 2 r2 2 From equation 2 it can be noted that initially 0 the value of the transmission ratio is relatively high and then gradually decreases as the string is twisted B Bidirectional Joint with Constant Radius Pulley First assume we have a conventional belt or cable trans mission system in which a cable is wrapped around a pulley driven by a rotational motor Fig 1 A with both sides of the cable routed around two rotational pulleys and connected to a load Provided that the pulley radius remains constant and equal on both sides motor rotation will result in symmetric winding unwinding of both left and right side cables which will allow control over the load position On the other hand assume one wants to replace the cable with a pair of twisted strings placed coaxially with the motor shaft Fig 1 B Strings can be installed in such a way that the rotation of the motor in one direction will result in contraction of one string and extension of the other and vice versa Thus once one string is fully twisted the other is fully untwisted However due to the nonlinear relationship between the angle of twisting and contraction described by 1 the fully twisted string would extend much faster than the opposite string would contract This would result in cable slack an excessive length of string remaining on the side opposite to the direction of motion This would reduce the tension on the joint and make it impossible to change the direction of motion until the slack was removed The magnitude of slack reaches its maximum in the middle of the range of motion ROM while its minimum is located at both ends of the ROM Slack can be calculated based on conventional TSA model 1 Assuming that both strings have the same untwisted lengths LA LB L and radius r and the motor ROM is 0 max the expected slack can be found as follows Xmax XA A XB B 3 where A 0 max and B max 0 are angles of twisting of agonist and antagonist strings XA A and XB B are respective contractions assumed to be positive at all times calculated according to 1 and Xmaxis the maximum string contraction occurring at angle max The simulation results given by model 3 are depicted in Fig 2 where one can see respective contractions of agonist and antagonist strings XAand XBduring twisting and the corresponding string slack To remove the slack one might twist both strings by half the motor ROM max 2 and install them symmet rically under pretension This would ensure that a certain amount of tension was applied to the strings at all times thus eliminating any possible slack However due to the difference in the contraction extension rates of fully twisted and fully untwisted strings the tension on them will be greatly increased towards the ends of the ROM Therefore the motor would need to exert additional torque to overcome it Increased tension on the strings would also lead to their premature wear whereas maximum payload on the joint could be signifi cantly diminished due to the loss of motor power used to overcome string in fi ghting Therefore applying pretension by twisting is not feasible as a practical solution Another way to remove the slack would be to linearize the ratio between the load displacement and motor angle making the string contraction rates constant over the entire ROM This could be achieved if one replaced the pair of constant radius pulleys depicted in Fig 1 B with nonlinear pulleys of which the radii varied in such way that they countered the nonlinear contraction characteristics of the respective twisted strings Providing guidelines for designing a nonlinear pulley of such shape is the main objective of this paper III VARIABLERADIUSPULLEYDESIGN A Synthesis of a Variable Radius Pulley Profi le In order to linearize the ratio between load displacement and motor angle we propose the system depicted schemat ically in Fig 3 Twisted string is connected to a grounded motor on one side and to a variable radius pulley VRP Motor Load Pulley String Wrapping Pulley A PulleyPulley Motor String Twisting B Fig 1 Conventional cable driven system A and single motor based bidirectional TSA driven system B 050100150 Motor Angle rad 0 1 2 3 4 5 6 Contraction and Slack cm XAgonist XAntagonist Slack Fig 2 Contraction of strings and slack in antagonist confi guration on the other by means of a slider and regular cable This way no part of the twisted string is wrapped around the pulley which could interfere with twist propagation 15 The string contraction is measured by a linear potentiometer A constant radius pulley CRP is placed co axially with the VRP and is rigidly connected to it so that both pulleys rotate together Another cable wound and unwound from the CRP drives the load The system operates as follows String contraction causes the VRP to rotate by an angle which also rotates the CRP by the same angle However bacause the VRP radius Rvrp is changing transmission ratio from string to pulley will also vary as intended Assuming the transmission ratios of TSA and pulley to be KTSAand KPulley respectively the total transmission ratio of the system from motor to load can be found simply as Ktotal KTSAKPulley 4 Now assume that we desire the total transmission ratio of the system to remain constant throughout the ROM Ktotal This suggests KPulley KTSA Using 2 and the fact Motor Constant and Variable Pulley Linear Potentiometer Cable Twisted String Load Force Fig 3 Schematic of experimental setup for single TSA that KPulley Rvrp Rcrp we can fi nd VRP radius Rvrpas a function of motor angle as follows Rvrp Rcrp r2 L2 r2 2 5 where r is the string radius B Maximizing Actuator Stroke One signifi cant limitation of twisted string actuators is the upper limit on string contraction It is generally accepted that a TSA can only contract by 30 of the original string length because further twisting results in unpredictable contraction inability of strings to return to their initial state upon untwisting and the potential severe shortening of the string lifetime 13 The proposed actuator however could have a larger stroke than an individual TSA because both and Rcrpare inde pendent design parameters Assuming that a certain actuator stroke Xloadis required one can see that Xload Rcrp Assuming the maximum pulley angle to be max 2 for a single rotation pulley one can note that the required CRP radius can easily be derived from the model above As for the desired transmission ratio one can show that Rcrp 6 Integrating equation 6 for the known initial and fi nal motor angles we can fi nd the required value of C Effects of String Radius and Pre twisting on the Variable Pulley Profi le One can notice from 5 that a number of parameters affect the VRP profi le However assuming that Rcrpand are constant and calculated as described in the previous section and that the untwisted string length L is also given two variables are left the string radius r and motor angle to determine pulley profi le Let us examine the effect of these variables on the resulting VRP shapes assuming maximum string contraction to be 30 of original length L First let us consider the effect of different string radii From 5 it follows that as the string radius increases the required VRP radius should increase Fig 4 shows differ ent simulated VRP profi les that yield the desired actuator transmission ratio Ktotal for a fi xed value of Rcrp 30 mm One can note how higher values of string radii correspond to larger required pulley profi les This highlights how important 20246 X cm 4 3 2 1 0 1 2 3 Y cm Joint rCRP rs 1 4 mm rs 1 6 mm rs 1 8 mm rs 2 0 mm Fig 4 Simulation results showing effects of variations in string radius on the VRP profi le with L 300 mm and RCRP 30 mm 2024 X cm 4 3 2 1 0 1 2 3 Y cm Joint rCRP p 0 rev p 3 rev Fig 5 Simulation results of effects of pre twisting on the variable pulley profi le with L 300 mm RCRP 30 mm and r 1 8 mm accurate knowledge of the string radius is for correct pulley synthesis Let us now consider how the motor angle affects pulley profi le One can note from 5 that if 0 the desired pulley radius becomes zero due to the transmission ratio of twisted string tending to infi nity as suggested by 2 Thus having fully untwisted string in the proposed actuator is not feasible as a practical solution and a certain pre twist angle pmight be desirable Due to the non linear nature of TSA transmission ratio a small pre twist may shift it signifi cantly from the singular point with negligible compromise in string contraction In addition it is often desirable to have a through hole in the middle of the pulley to accommodate a hinge joint which also calls for introduction of pre twist Pre twisting assumes that at the beginning of operation a string is installed after being twisted by a certain angle p Motor Variable Pulleys Sliders Linear Potentiometer Cable Gears Constant Radius Pulley with Encoder Load Force Twisted String B Twisted String A Fig 6 Schematic diagram of single motor based bidirectional twisted string actuator Motor Contant and Variable Radius Pulleys Cable Twisted String B Linear Potentiometer Twisted String A Encoder Slider Gears Load Force Fig 7 Experimental setup for bidirectional actuation experiments pre twisting angle instead of being in its fully untwisted condition In this case assuming for convenience that zero motor angle 0 corresponds to p one can simply augment equations 2 and 5 so that they become KTSA pL2 s r2s p 2 r2 p 7 RVRP RCRP r2 p pL2 s r2s p 2 8 We carried out simulations under the same conditions as in the previous case whereas the string radius was kept constant at r 1 8 mm for different values of the pre twisting angle p Fig 5 shows the results As expected it was found that pre twisting simply shifts the initial point of the VRP profi le away from the origin along the same curve This way one can calculate the pre twisting angle required to have a through hole of the desired diameter or to increase the initial contraction rate IV EXPERIMENTALEVALUATION A Experimental Setup To validate the performance of the proposed VRP based twisted string actuation system we manufactured the exper imental setup shown schematically in Fig 3 However this layout has one important drawback in that it is unidirectional meaning that it relies on external force to untwist the string To improve on this structure and to make it bidirectional we proposed and experimentally evaluated a