Energy Efficiency Improvement of a Robotic Finger With Ultra High Molecular Weight Polyethylene Gear

Improving energy efficiency of robots is an important issue for diffusion of robots in society. For reducing the energy consumption of robots, we focused on the gear weight and friction during drive, and investigated Ultra High Molecular Weight Polyethylene (UHMW-PE) for the robot joints as a lightweight, low friction, and high impact strength material. A simple UHMW-PE gear has already been proposed, and the friction and wear reduction effects of the gear alone have been verified. However, the energy efficiency improvement has not been investigated. We designed UHMW-PE gears for comparing to the conventional metal (CAC502) gear. Each gear was incorporated into a humanoid robot finger joint, and the energy consumption when the finger bended was compared. The UHMW-PE gear with excellent self-lubrication reduced energy consumption in the robot finger by around 3%.

Most of the energy consumption during robot operation is 23 motor power rather than the power consumption of the robot 24 The associate editor coordinating the review of this manuscript and approving it for publication was Gerardo Flores . controller, and it increases especially as the robot becomes 25 larger and heavier. Therefore, in order to reduce the energy 26 consumption of the robot itself, the weight reduction of 27 the robot itself greatly contributes. In particular, the frame 28 part of the robot needs to be strong enough to support its 29 own weight, and metal is often used for life-sized robots 30 [1], [2]. However, in recent years, plastics and carbon fiber 31 reinforced plastics have also been used for further weight 32 reduction. Gouaillier et al. have developed a compact and 33 lightweight humanoid robot, Nao, by using plastic to reduce 34 weight [3]. In addition, as an improvement in the design of 35 structural members, a method using topology optimization 36 as a shape design using optimization calculation has been 37 devised in order to reduce the weight while maintaining the  structure consisting only of carbon and hydrogen atoms. 98 These characteristics suggest that UHMW-PE is suitable for 99 gears of robots in high loads or high speeds, and is expected to 100 reduce energy consumption due to its lightweight and sliding 101 properties.

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This study has the main contribution to robotics field as 103 below. By installing the UHMW-PE gear, a reduction of 104 about 3% in energy consumption was achieved by reducing 105 friction in addition to reducing the weight of the robot joints. 106 A simple UHMW-PE gear has already been proposed, and the 107 friction and wear reduction effects of the gear alone have been 108 verified. However, no verification of energy consumption 109 has been conducted on a robot joint driven by a high load. 110 Together with weight reduction, low friction is effective in 111 reducing the energy consumption of robots.

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This paper is organized as follows. In Section 2, 113 we describe the design of the UHMW-PE gear and the robot 114 for evaluation of the gears, and the experiment method. 115 In Section 3, we present experimental results. In Section 4, 116 we discuss the limitation and novelty of this work. Finally, 117 in Section 5, we present conclusions and propose future 118 work.

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A. MATERIALS 121 UHMW-PE materials used in this study were HI-ZEX 122 MILLION TM (0.93 g/cm 3 ) and LUBMER TM (0.97 g/cm 3 ) 123 supplied from Mitsui Chemicals respectively (Table.1) 124 [20], [21]. HI-ZEX MILLION TM is a typical powdered 125 UHMW-PE, and its gears for robot joints was made by 126 cutting blocks. LUBMER TM is a special UHMW-PE that 127 can be injection molded or extrusion molded with typical 128 characteristics of UHMW-PE, excellent sliding properties 129 and abrasion resistance. UHMW-PE is generally molded by 130 compressing or cutting, because its melt viscosity is so high 131 that injection or extrusion are difficult. For gears in robots 132 joint, LUBMER TM is expected to reduce energy consumption 133 and simplify gear molding. In addition to being easier to 134 process than typical UHMW-PE, LUBMER TM is a material 135 that is also consistent with a circular economy perspective 136 because it can be recycled through melt-blending. In this 137 study, the LUBMER TM gear is made by cutting its blocks 138 same as HI-ZEX MILLION TM in order to unify sample 139 conditions.

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To validate the UHMW-PE gear, a worm gear to drive a 142 robotic finger was fabricated in UHMW-PE in this study. 143 We have developed a humanoid robot for achieving human-  as tooth module, tooth angle, and combination of materials 181 influence to friction between the worm and worm wheel con-182 tact area [25]. Moreover, operational conditions are affected 183 by the pressing force between the worm and worm wheel, 184 torque, speed when driven, and lubrication [26], [27]. Esti-185 mation of gear friction coefficient is complicated problem 186 and various methods have been proposed in recent years [28], 187 [29], [30]. In order to match the experimental conditions, each 188 VOLUME 10, 2022 by equation (3) from the model of the electric motor [31].
where, R is the electrical resistance of the motor, k is the 217 counter electromotive force constant, ω (t) is the number of 218 revolutions of the motor at time t, and L is the inductance of 219 the motor. The output torque τ (t) of the motor is calculated 220 by equation (4).
where, k t is the torque constant of the motor. In theory, the 223 torque constant matches the counter electromotive force con-224 stant k. When using a low-inductance motor, the inductance 225 effect is negligible. By substituting into equation (1), power 226 consumption from the current and rotation speed of the motor 227 is calculated in equation (5).
In the experiment, equation (5) was used to calculate the 230 power consumption of the motor, and total energy consump-231 tion was calculated by integral calculations as equation (6). 232 where, E is total energy consumption in Joule, and T is 234 total time of an experiment. The specification of the motor 235 used in the experiment is shown in Table 3. The motor was 236 equipped with an incremental encoder and was connected to 237 a motor controller. We used a motor controller ELMO Gold 238 Twitter (ELMO Motion Control Inc.). As a simple bending 239 motion, time-series angle reference was set for rotating the 240 worm wheel 35 deg in uniform acceleration and deceleration 241 (Fig. 6). The motor controller controlled the motor speed 242 according to the preset motor rotation speed command with 243 proportional-integral-derivative (PID) controller. The PID 244 control gain was tuned for a motor without a gear using the 245 software of Elmo Application Studio II. The motor controller 246 acquired the motor angle, angular velocity, and current data 247 and recorded them every 0.1 millisecond.

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Experiments using each gear were performed 5 times. 249 Generally, when using a metal gear, lubricating oil is required, 250 but the UHMW-PE gear can be used oil-less due to its self-251 lubrication. In this experiment, a dry film lubricant for gears, 252 GJS-0901 (Kohara Gear Industry Co.), was applied only for 253 metal gears to improve lubricity. The experimental conditions 254 are summarized in Table 4.

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The measured average current data during the experiment 257 is shown in Fig. 7. The standard deviations are also shown 258 in the graph and were very small for all conditions. The   show that the current consumption increased slightly when 263 HI-ZEX MILLION TM was used compared to that of the 264 metal gear, while the current consumption was reduced when 265 LUBMER TM was used. Also, compared to the metal gear, 266 the total energy consumption was increased around 1% in the 267 case of HI-ZEX MILLION TM , decreased around 3.4 % in the 268 case of LUBMER TM .

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The energy consumption of the LUBMER TM gear was lower 271 than that of the metal gear, as expected. On the other hand, 272 the energy consumption of the HI-ZEX MILLION TM gear 273 was slightly higher than that of the metal gear, but this may 274 be due to the fact that the metal gear was lubricated while 275 VOLUME 10, 2022 LUBMER TM gears will greatly reduce the overall weight of 332 the robot. It also affects the energy efficiency improvement. 333 Power consumption of a joint j of a robot is calculated in 334 equation (7).
where,P j (t) is the power consumption of the j joint at time t, j 337 is the number of the joint, t is the time in the experiment, τ j (t) 338 is the torque of the j joint at time t, and ω j (t) is the angular 339 velocity of the j joint at time t. In general, the equation of 340 motion of the robot joint is given by where M (q j ) is the inertial matrix; H (q j ,q j ) is the Coriolis 343 and centrifugal terms, G(q j ), q j is the coordinate of the j joint. 344 The power consumed in each joint is calculated, and then 345 the total power consumption is calculated by summing all 346 joints power consumptions [36]. In particular, the reduced 347 weight of the fingers and hands in this study contributes to 348 a significant reduction in the moment of inertia of the entire 349 arm when the robot moves the arm because the weight of the 350 part far from the joint is added to the moment of inertia by 351 the square of the distance between the mass and the joint. 352 If the moment of inertia is reduced, the torque that must 353 be exerted by the elbow and shoulder joints that move the 354 arm is greatly reduced, thus reducing energy consumption. 355 Equation (7)

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Since 2019, he has been a Guest Researcher 529 with the Waseda Research Institute for Science 530 and Engineering, Waseda University, Japan. Since 531 2022, he has been the CEO of the hide kasuga 532 group founded, in 2012 as a material think tank as 533 well as an Industrial Strategy Advisor for Nagano City. His research interests 534 include circular economy, environmental chemistry, formulation, recycling 535 technology, and material branding.  He is currently a Professor with the Department 547 of Modern Mechanical Engineering as well as 548 the Director of the Humanoid Robotics Institute, 549 Waseda University. His current research interests 550 include humanoid robotics and its applications in 551 medicine and well-being, such as the biped walk-552 ing/running humanoids, the emotion expression humanoids, the flute player 553 humanoids, the ultrasound medical inspection robots, and the airway man-554 agement training humanoids.