IROS2019国际学术会议论文集 1529

Effect of Vibration on Twisted String Actuation Through Conduit at High Bending Angles Donghyee Lee1 Igor Gaponov2 Jee Hwan Ryu3 Abstract This paper studies an effect of vibration on twisted string actuation through conduit at high bending angles In our previous work 1 we have demonstrated that twisted string actuators can be used to transmit power even at signifi cant defl ection angles of the conduit However several undesirable effects namely pull back hysteresis and chattering were present during actuation due to friction between strings and the internal sheath of the conduit This paper reports the results of experimental study on effects of vibration on twisted string actuation inside defl ected conduits We have demonstrated that applying vibration generated near natural frequency of the system during the later stages of twisting and untwisting cycles helped reduce pull back and hysteresis and increase string contraction In case when sheath was defl ected by 180 under a constant load of 3 kg we were able to achieve over 70 decrease in pull back and 30 decrease in hysteresis compared with no vibration case Keywords Tendon Wire Mechanism Vibration Friction I INTRODUCTION Twisted string actuators TSAs are an interesting alter native to conventional transmission systems due to their cheap light mechanically simple and compact nature 2 The basic operation principle behind TSA is that strings contract when twisted generating large pulling forces for comparatively low twisting torques Thanks to their unique benefi ts TSA have found many applications in various areas of modern engineering and robotics including mobile robots 3 exoskeletons 4 5 and robot hands 6 One of the most signifi cant advantages of TSAs is their mechanical fl exibility In order to take full advantage of this strings must be allowed to operate with non zero curvature However in this case there can be potential friction and wear of strings due to the contact of them with environment One possible solution is putting them inside of a fl exible conduit as it is done in Bowden cables However under larger than certain amount of defl ection twisted strings behavior starts to deviate signifi cantly from conventional mathematical model Since it is fairly complicated to propose a generalized accurate model describing twisted string in contact with defl ected conduit it might be necessary to This research was partially supported by the project Development of core teleoperation technologies for maintaining and repairing tasks in nuclear power plants funded by MOTIE and by the NRF Korea grant MSIP No NRF 2016R1E1A1A02921594 1School of Mechanical Engineering KOREATECH Cheonan South Korea wlffjt22 koreatech ac kr 2Faculty of Computer Science and Engineering Innopolis University Innopolis Russia i gaponov innopolis ru 3Dept of Civil and Environmental Engineering KAIST Daejeon South Korea jhryu kaist ac kr minimize the friction acting on the string to mitigate potential negative effects as much as possible Palli et al have proposed a mathematical model describing twisted string in contact with environment in several points along its length 7 Although this model could describe string behavior comparatively well the authors did not address how to mitigate the friction effects Suthar et al reported a preliminary study on twist propagation inside a continuous conduit 1 This work established that when strings are twisted inside a continuous conduit with curva ture negative effects caused by friction appear namely pull back and chattering and a method to mitigate those effects is required On the other hand there exists an abundance of literature dedicated to study the effects of vibration on friction 8 9 10 In addition a work by Kuribayashi et al described how microscopic vibration could reduce friction between sliding wire and a conduit 11 However to the best of our knowledge there has been no study related to the effects of vibration on twisted string inside a conduit Unlike previous studies on the topic which tried to observe and model behavior of twisted string inside curved conduit we wanted to actively intervene and alleviate negative effects caused by friction as much as possible In this paper we investigated feasibility of using vibration to reduce friction acting between conduit and twisted string We have exper imentally studied the behavior of TSA with and without vibration for two defl ection angles of the sheath 90 and 180 degrees In addition we have evaluated the effects of various vibration parameters frequency source location timing and pattern on twist propagation Based on the results of preliminary study we have designed and experimentally tested optimal vibration pattern which requires vibration only 15 of the operation time Application of this vibration pattern helped decrease undesirable pull back effect by 70 and increase actuator stroke by nearly 15 II BACKGROUND A Kinematic Model of Twisted String This section describes conventional mathematical model of a twisted string which is derived from assumption that an infi nitesimal section of a cable is uniformly twisted thus forming a helix 12 13 A schematic representation of a section of twisted string is given in Fig 1 To derive the model we assume that length of loaded string and its radius are denoted by Lcand r respectively and when the string is twisted by motor for an angle it contracts by X amount Contracted length of the string can 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE5965 Fig 1 Geometric scheme of TSA R L Fig 2 Friction force diagram of twisted string inside conduit be calculated from the unwound geometrical helix model as follows X q L2 c 2r2 1 The relationship between angle of twisting and the linear contraction of string X can therefore be written as X Lc q L2 c 2r2 2 This mathematical model can be used predict string con traction X for small curvatures of conduit with low friction coeffi cient However experiments demonstrated that it will not be suitable to describe twisting behavior for conduit curvatures exceeding 90 as the behavior of the string will deviate rapidly from the model due to friction B Friction between Twisted String and Conduit To have a better insight into behavior of twisted string inside a conduit with signifi cant curvature let us look at Fig 2 We assume that a conduit of length L is defl ected by angle along the path with constant curvature radius R When a string is twisting and contracting inside conduit in the direction corresponding to input force fin friction force fr resists its contraction and twist propagation in that direction The friction is determined by respective reaction force fn This model has been used in the previous preliminary study that demonstrated that propagation of twisting inside the sheath was impeded 1 The authors have also highlighted Motor String Vibrator 180 degree Accelerometer Pulley connected to the load PTFE tube Vibrator Accelerometer Fig 3 Experimental setup A DC motor is used to twist the string inside a conduit with vibration motor and accelerometer attached to it The other end of the string is attached to payload through a pulley the following new effects taking place when twisting occurs inside a conduit with signifi cant curvature Pull back At the start of every new twisting cycle the load undesirably recoils back from the motor at fi rst before moving towards it again This is due to the fact that initial twisting actually untwists the motor side string that coiled in the opposite direction during the preceding untwisting cycle The magnitude of this load displacement from the start until the point when it begins to move toward the motor again is called pull back The magnitude of pull back is larger for higher curvatures since increasing friction prevents larger sec tions of the string from untwisting properly Hysteresis Like every other power transmission mech anism twisted string behavior will exhibit a certain amount of hysteresis due to non 100 effi ciency De spite hysteresis being comparatively small for straight twisted strings it will become larger with increase in conduit s curvature In addition a dead zone will appear in the regions where motor switches its direction due to friction In this study we used vibration to mitigate negative effects caused by friction on twisted string while studying string behavior in different vibration modes The next section discusses experimental setup and procedures used in this research III EXPERIMENTALSETUP ANDSCENARIO A Experimental Setup In order to investigate the effect of vibration on the input output characteristics of the twisted string though a conduit under curvatures we have conducted an experimental study using the test setup shown in Fig 3 EC motor Maxon 45 250 Watt equipped with a 500 CPT encoder 3 channels linedriver RS 422 HEDL 9140 is rigidly mounted on a profi le frame A PTFE tube used in experiments had inner diameter of 10 mm and a thickness of 1 mm while its length was 500 mm A pair of braided Dyneema strings with the diameter of 1 mm and length of 900 mm were attached to the motor and fed through the conduit to a load on the other side Different loads ranging between 1 and 5 kg were hung on the strings during the experiments Defl ection angle of the conduit could be changed 0 and 180 degrees with constant radius of curvature set at 220 mm 5966 For this study we selected two fi xed values of defl ection angles of 90 and 180 A vibration motor MB2025 1268V 6880rpm was installed on curved area of the conduit To measure vibration frequency and amplitude we attached accelerometer ADXL335 GY61 next to the vibration motor A linear incremental encoder HEDS 9740 was also installed at the load side to measure string contraction To prevent initial slack in the TSA strings were pre tensioned Following this proposed step twisting of the strings result in their contraction which pulls the constant load toward the motor Control system ensured motor was tracking sinusoidal input trajectory during all the experiments B Experimental Procedure To thoroughly evaluate effects of vibration on twist prop agation inside curved conduit we have studied input output position relationships of twisted strings for 2 different cur vatures of conduit various load weights different vibration frequencies and triggering instances modes All of these were then compared to no vibration case of TSA operation It should be noted that selecting proper materials for string and conduit is very important to minimize the friction Some studies have reported the combination of ultra high molecular weight polyethylene UHMW PE and polytetrafl uoroethy lene PTFE materials has one of the lowest known fric tion coeffi cients which is on the order of 0 04 0 06 14 Based on this study we selected stings manufactured from Dyneema a material made of polymer polyethylenefi ber and a conduit made of PTFE due to its self lubrication prop erty extremely low friction coeffi cient and characteristics in which vibration is well transmitted even at low frequencies In addition it was shown that adding vibration helps decrease friction coeffi cient with increase in vibration amplitude and therefore applying appropriate levels of vibration may help mitigate negative effects of friction even further 15 To maximize the effect of friction on the conduit we have installed both vibration motor and accelerometer in the middle of the sheath where friction was expected to have the biggest impact on twisting Before respective experimental trials preliminary tests were conducted to determine reso nance frequency of the system In these tests string was twisted inside the conduit defl ected by 90 degrees under constant load of 2 kg and 3 kg and we swept frequency range up until 500 Hz while measuring sheath s vibration amplitude After collecting the data we performed fast fourier transform FFT to determine resonant frequency as shown Fig 4 and Fig 5 Results of natural frequency tests are summarized in Table I One can notice that resonant frequency was sensitive to the change in external load but showed less dependency on the changes in curvature IV EXPERIMENTALEVALUATION A Effect of Vibration on Input Output Position Characteris tics Our fi rst experiment was intended to verify the effect of vibration on basic input output position characteristics 100101102 35 30 25 20 15 10 Freq Hz dB Resonant frequency Fig 4 Frequency response of sheath under 90 defl ection and 2 kg payload Natural frequency is found to be 56Hz 100101102 35 30 25 20 15 10 Freq Hz dB Resonant frequency Fig 5 Frequency response of sheath under 90 defl ection and 3 kg payload Natural frequency is found to be 76Hz of TSA under defl ection To do this we have measured input motor angle and output string contraction positions of the TSA while vibration was on during both twisting and untwisting The same experiment was repeated with 4 different frequency values no vibration natural frequency one in higher than natural frequency and one in lower than natural frequency In the experiments the string was twisted and untwisted repeatedly by a fi xed amount under constant load 2 kg and resulting input output position curves are plotted in Fig 6 for the conduit curvature angle of 90 degrees After the fi rst cycle was completed behavior of the string in all subsequent cases converged to a steady limit cycle with a certain amount of hysteresis present All the curves depicting this limit cycle are averaged data based on 5 full cycles Measured input output position curves are shown in Fig TABLE I RESONANT FREQUENCY FOR DIFFERENT CURVATURES AND LOADS CurvatureLoadResonant frequency 90 1 kg33 Hz 2 kg56 Hz 3 kg76 Hz 180 1 kg42 Hz 2 kg64 Hz 3 kg77 Hz 5967 05101520 0 5 10 Motor angle rot Contraction mm No vibration 33 Hz Lower than resonant frequency 56 Hz Resonant frequency 91 Hz Higher than resonant frequency Twisting Untwisting 1718192021 12 5 13 13 5 14 024 0 0 5 1 1 5 Fig 6 Effects of vibration at different frequencies on twisted string under 90 defl ection and 2 kg payload 6 When twisted inside a conduit a string behaves as follows Points 1 2 During the fi rst cycle twists start to prop agate along the conduit from the motor to the load and the load starts to move Point 1 corresponds to the initial untwisted confi guration of the TSA while point 2 represents its maximally contracted state Points 2 3 This segment corresponds to the fully un twisting cycle of TSA When untwisting stops at point 3 a certain number of twists remains inside the conduit on the load side of the string due to existing friction Because of this the motor side of the string remains twisted in the opposite direction therefore the load does not return to its original position Limit cycle 3 4 2 After the fi rst cycle twisted string behavior converges to a stable limit cycle Between points 3 and 4 pull back occurs which is undesirable recoil motion opposite to the motor even with the twists of strings After that contraction curve loosely repeats the fi rst cycle As was briefl y mentioned in Section 2 pull back phe nomenon happens due to the presence of opposite directional twists in the string after the previous cycle High magnitude of pull back difference in heights between points 3 and 4 in Fig 6 is undesirable because this causes extension of the string instead of expected contraction and thus the actuator is poorly controllable in this region In addition point 3 should be brought down as close to point 1 as possible because vertical distance between them corresponds to the loss of effective stroke in twisted string due to friction whereas this stroke could have been translated into load s motion instead One can notice from inlets on Fig 6 that application of vibration affected TSA characteristics quite signifi cantly Firstly it helped decrease both pull back magnitude and lost stroke with vibration around the resonant frequency having seemingly the best effect for both providing about 40 in pull back reduction Secondly it allowed the string to contract further than in case without vibration However shortly after the start of untwisting point 2 contraction briefl y increased in cases with vibration which is an effect we would like to tentatively call overshoot This overshoot was not observed in no vibration experiments Lastly vi TABLE II DECREASE IN PULL BACK AND LOST STROKE WITH VIBRATION LoadFrequencyPull backStroke loss Low 20 Hz5 17 Resonant 33 Hz26 33 1 kg High 91 Hz9 7 22 Low 33 Hz20 28 Resonant 56 Hz30 34 2 kg High 91 Hz15 28 Low 56 Hz28 34 Resonant 76 Hz40 73 3 kg High 106 Hz30 30 Low 56 Hz26 32 Resonant 106 Hz40 64 4 kg High 140 Hz33 45 Low 56 Hz15 33 Resonant 110 Hz32 80 5 kg High 140 Hz20 43 bration helped decrease hysteresis in string behavior quite signifi cantly We repeated the same experiment for different load con ditions and observed similar trends Experimental results are summarized in Table II Negative sign in the Stroke loss column corresponds to decrease in its value positive effect and vice versa It can be seen from these data that applying vibration to a sheath with twisted string inside can positively affect operation of TSA since vibration effectively reduces the friction coeffi cient between the string and the sheath Generating vibration with frequencies close to natural resonant frequencies of the system seemed to have the most pronounced effect One can note that application of continuous vibration during TSA operation resulted in 20 30 reduction of pull back and up to 70 80 reduction in lost stroke However these experiments could not provide any data on whether vibration should be continuous e g always on dur ing operation or it can be turned on selectively depending on current operation point of the actuator This experimental scenario was investigated and results are reported in the following section B Effect of Intermittent Vibr