IROS2019国际学术会议论文集 2411

Abstract The use of high capacity motors and harmonic drives increases the manufacturing cost and the energy consumption of the robot It is well known that most motor torques are used to support the robot mass and payload To deal with this problem we propose a wall mounted 3 DOF roll pitch pitch counterbalance mechanism CBM Unlike previous CBMs used for floor mounted industrial robot arms the proposed CBM can be applied to wall mounted robots in which the first three joints are all coupled and affected by gravity This mechanism is composed of pure mechanical components such as coil springs differential gear structure and belt pulley system A 6 DOF robot arm equipped with the proposed CBM was fabricated to verify the performance of gravity compensation It is shown that the proposed 3 DOF CBM can effectively compensate for gravitational torques thus drastically reducing the motor torques required to operate the robot I INTRODUCTION The use of high capacity motors and speed reducers is essential for industrial robots to handle large payloads in a large working space However such high capacity actuators tend to increase the manufacturing cost and operation cost of the robot To deal with these problems several types of counterbalance mechanisms CBM or passive gravity compensators have been developed to effectively support the robot mass and payload and thus reduce motor torques required to operate the robot Much research has been done on various mechanisms to compensate the gravitational torques of the robot arm using mechanical components such as a counterweight coil spring gas spring slider crank mechanism and so on 1 4 However most of such mechanisms can only compensate the gravitational torque on a single pitch joint which makes it difficult to apply this method to a multi DOF robot arm Some researchers proposed gravity compensators which were applicable to 2 DOF pitch pitch joints using a parallelogram linkage or a belt pulley structure 4 8 Nearly perfect gravity compensation could be achieved with these mechanisms for the robot having consecutive pitch joints subject to gravitational torques However these mechanisms were limited to floor mounted robot arms and could not be applied to the wall mounted robot arm such as a humanoid robot arm 9 10 This work was supported by IITP grant funded by the Korea Government MSIT No 2018 0 00622 Won Bum Lee and Tae Jung Kim are with the School of Mechanical Eng Korea University Seoul Korea e mail tiger1118 korea ac kr Byung Yoon Moon is with LG Electronics PRI Gyeonggi do Korea Jae Bok Song corresponding author is a Professor of the School of Mechanical Eng Korea University Seoul Korea Tel 82 2 3290 3363 fax 82 2 3290 3757 e mail jbsong korea ac kr In this study we propose a 3 DOF counterbalance mechanism that is applicable to a wall mounted 6 DOF robot arm It is very difficult to compensate for the gravitational torques applied to the first three joints of the wall mounted robot arm because these torques change continuously as a function of both roll and pitch joint angles Therefore a special CBM should be devised for perfect gravity compensation The proposed CBM consists of pure mechanical elements such as coil springs slider crank mechanisms and timing belt pulley structure Furthermore a 6 DOF wall mounted robot arm based on the proposed 3 DOF CBM is also developed to verify the performance of gravity compensation The motor torques required to operate the robot will be examined for the robot with and without 3 DOF counterbalancing This paper is organized as follows Section II discusses the principle of the wall mounted roll pitch pitch CBM The design of the robot arm using the proposed CBM is presented in Section III In section IV counterbalancing performance of the robot is investigated through experiments Finally conclusions are drawn in section V II COUNTERBALANCE MECHANISM A Counterbalance for Pitch Joint A gravitational torque Tg of a 1 DOF link shown in Fig 1 is described by sin gc Tmgl 1 where m is the mass of the link lc is the distance between the joint and the center of mass and is the joint angle measured from the reference plane that is perpendicular to the ground This gravitational torque applied to a pitch joint can be compensated by a counterbalance mechanism CBM based on a slider crank mechanism as shown in Fig 1 a and b As the link rotates the connecting rod pulls the slider which is constrained to move along the link and compresses the spring The spring compression s is given by 0 coscos crcr rlrlss 2 where lcr is the length of the connecting rod so is the initial spring compression and other variables are defined in the figure The force Fcr applied to the connecting rod is given by cos cos crs FFks 3 and the distance lm is given by sin m lr Therefore the compensation torque or counterbalancing torque Tc can be computed as Wall Mounted Robot Arm Equipped with 3 DOF Roll Pitch Pitch Counterbalance Mechanism Won Bum Lee Byung Yoon Moon Tae Jung Kim and Jae Bok Song Senior IEEE 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 IEEE3571 0 coscos sin cos crcr ccr m kr rlrls F lT 4 s0 s lc m g k Fs Fcr r lcr Slider Spring Connecting rod lm Torque Nm 018090 0 Tg Tc TgTc 20 10 a b c Spring Reference plane Figure 1 Counterbalance mechanism based on slider crank mechanism a total diagram b closed up diagram of the connecting rod and c comparison between the gravitational torque and compensation torque The compensation torque Tc looks quite different from the gravitational torque Tg in Eq 1 However the following two assumptions are met these torques are of the same form Assumption 1 lcr r 5 Assumption 2 0cr rsl 6 According to assumption 1 becomes very small thus leading to cos 1 Then Eq 4 can be simplified to 0 cos sincos sin c Tkr rrs 7 Since sin lcr sin holds Eq 7 becomes 0 cos cos sin ccr cr kr Trrslr l 8 Substitution of Eq 6 into 8 yields 222 cos sinsin ccrcr cr kr Tlrkrl l 9 Now that both torques in Eqs 1 and 9 are a function of sin successful gravity compensation can be achieved by the following relation ccr mglkrl 10 Note that assumption 2 can be easily satisfied but assumption 1 is very difficult to satisfy Therefore the shape of Tc is not an exact sine wave but an approximate one which means that perfect gravity compensation cannot be achieved However this error in gravity compensation does not cause any trouble because the error can be compensated easily by the motor torque during the robot operation The design parameters r lcr k and s0 of the CBM can be adjusted to satisfy Eq 10 for given parameters m and lc of the link B Counterbalancing for Pitch Pitch Joints A floor mounted 3 DOF robot arm having roll pitch pitch joints along with two CBMs mounted on the pitch joints is shown in Fig 2 The gravitational torques Tg2 and Tg3 applied to joints 2 and 3 respectively are described by 222322 sin gc Tm glm gl 11 3333 sin gc Tm gl 12 where m2 and m3 are the mass of links 2 and 3 respectively and 2 and 3 are the angles of joints 2 and 3 measured from the reference planes RP respectively which are always in the direction of gravity Note that Tg1 0 because joint 1 is not affected by gravity Joint 2 Joint 3 m3m2 CBM 1 Belt pulley mechanism RP 1 RP 2 3 Joint 1 l2 RP 2 2 Link 1 Pulley 1 Pulley 2 2 lc3lc2 l3 Link 2Link 3 CBM 2 3 Figure 2 Floor mounted robot arm having roll pitch pitch joints and two counterbalance mechanisms The reference plane RP 1 can be easily set up on the ground and RP 2 is provided by a belt pulley structure which functions as a parallelogram mechanism 4 8 As shown in Fig 2 both RP 1 and RP 2 are always kept perpendicular to the ground for any robot configuration If each CBM is installed with respect to its own RP 1 DOF counterbalancing Fig 1 can be extended to multi DOF counterbalancing Furthermore the belt pulley structure can provide a path along which the torque Tc3 compensated by CBM 2 can be transmitted directly to the ground Without this path the gravitational torque at joint 2 becomes the sum of Tg2 and Tg3 Successful 2 DOF counterbalancing leads to Tg2 Tc2 and Tg3 Tc3 and thus the following relations are obtained 22321 11ccr m glm glk rl 13 332 22ccr m glk r l 14 Therefore the design parameters of CBMs can be determined to satisfy Eqs 13 and 14 This principle of 2 DOF counterbalancing explained above can be applied to other types of multi DOF counterbalancing C Counterbalancing for Roll Pitch Joints Unlike a robot arm with pitch pitch joints discussed in the previous section if the arm is mounted to the wall e g humanoid robot arm then a roll joint as well as a pitch joint is affected by gravity thereby requiring another type of gravity compensation device As shown in Fig 3 when the roll and pitch joints are rotated by r and 2 p respectively in the wall mounted 2 DOF arm composed of roll pitch joints having mass m and center of gravity distance lc the gravitational torques applied to each joint are 3572 112 sincos gc Tmgl 15 212 cossin gc Tmgl 16 Since the gravitational torques are affected by both joint angles and are expressed by the product of sine and cosine functions the CMBs presented before are not applicable to this case Roll Pitch z x y 2 m lc 1 Figure 3 Wall mounted 2 DOF robot arm with roll pitch joints This problem can be solved by integrating a differential gear structure into the CBM as shown in Fig 4 In the figure three bevel gears are connected in a differential gear structure and gears A and B are equipped with slider crank based CBMs A and B respectively Gear C is fixed to the wall Roll rotation is realized by rotating link 1 around gear C At this time gears A and B are turned in the opposite directions by the differential gear structure Pitch rotation is realized by rotating link 2 around the rotation axis of gears A and B without rotation of these gears Gear A Gear B Gear C Fixed y x Wall CBM B CBM A Joint 1 Roll Joint 2 Pitch Link 1 Link 2 Figure 4 Counterbalance mechanism for wall mounted 2 DOF roll pitch joints using differential gear structure Fig 5 a shows the schematic diagram of CMBs A and B viewed in the direction of the y axis in Fig 4 when the system undergoes roll rotation 1 and pitch rotation 2 A new coordinate frame x y z is created by roll rotation and thus the y axis is now the rotation axis of a pitch joint Roll rotation of 1 causes gears A and B to turn by 1 in the opposite direction because gear C is fixed Then the angles between the reference line A or B and link 2 are given by 21A 17 21B 18 From Eq 9 the compensation torques generated by each CBM are given by sin 100 W motors for joints 1 and 2 and a 50W motor for joint 3 whereas a robot having 5 kg payload and 0 9m reach usually requires 400 W motors for joints 1 and 2 and a 200 W for joint 3 Therefore the counterbalance robot can achieve the same performance even with motors with only 25 capacity compared with robots without counterbalancing TABLE I DESIGN PARAMETERS OF THE SLIDER CRANK BASED CBMS Joint CBM Design parameters r mm lcr mm k N mm s0 mm Joint 2 CBM 1 28 80 15 7 52 Joint 3 CBM 2 20 70 16 2 50 Joint 1 Joint 2 Joint 3 Base CBM 1 CBM 2 Bevel gear Joint 4 Joint 5 Joint 6 Figure 10 Wall mounted 6 DOF robot arm with 3 DOF roll pitch pitch counterbalance mechanism y g z 1 x 2 3 45 45 45 A 00 9 00 9 00 9 TgTc A A B B B C C C 3 3 3 6 6 6 A B C Time s Time s Time s T Nm T Nm T Nm 80 40 80 40 80 40 Joint 1 Joint 2 Joint 3 Figure 11 Torque compensation by the wall mounted roll pitch pitch counterbalance mechanism IV VERIFICATION In order to investigate the performance of the proposed counterbalance robot arm a series of experiments were conducted to compare the torque load of the robots with and without the CBMs As shown in Fig 12 and Table II the joint torque load was analyzed during 3 task motions where joints 1 to 3 rotate sequentially The joint velocity and acceleration were set to 15 s and 30 s2 respectively while a maximum payload of 5 kg was attached to at the end of the robot Since it was impossible to drive the robot with 50 or 100W motors without counterbalancing the experiment without counterbalancing was conducted with 400 W motors for joints 1 and 2 and a 200 W motor for joint 3 3 2 1 Motion 1Motion 2Motion 3 Figure 12 Task motions for the experiments 3575 TABLE II TASK CONDITIONS OF THE EXPERIMENTS of task Angular displacement 1 2 3 1 0 45 45 2 45 3 90 Fig 13 shows the motor torques of the counterbalance robot during tasks 1 to 3 where the motor torque was measured based on the motor current motor torques from the verification experi ments were divided with desired torques and friction torques in figure 13 and 14 depicting cases without and with counterbalan cing respectively It is seen that the gravity compensator significantly reduced the torque loads for all tasks and motions Table III shows the maximum torques with and without counterbalancing As shown in the table the maximum torques at joints 1 2 and 3 were reduced by 74 64 and 55 respectively when counterbalancing was active Due to friction and inertial torques these reduction rates were not as high as the simulation results of 95 in Fig 13 but they could still dramatically reduce the required motor capacity These experiments confirm that the proposed 3 DOF counterbalance mechanism can effectively compensate the gravitational torques of a wall mounted robot arm thereby reducing the torque load and allowing the use of low capacity motors 369123691236912 Time s Time s 100 0 Torque Nm Time s 00 a A B C 100 With counterbalancingWithout counterbalancing Time s Time s 100 0 Torque Nm Time s 00 100 b Time s Time s 100 0 Torque Nm Time s 00 100 c 000 000 000 369123691236912 369369123691212 Figure 13 Measured torques for a task 1 b task 2 and c task 3 TABLE III REDUCTION IN JOINT TORUQE WITH COUNTERBALANCING Joint Maximum torques Nm Reduction rate Without CBM With CBM Joint 1 96 25 74 Joint 2 89 32 64 Joint 3 42 19 55 V CONCLUSION In this study we developed a wall mounted 6 DOF robot arm equipped with a 3 DOF roll pitch pitch counterbalance mechanism The performance of the proposed device was verified based on simulations and experiments The following conclusions are drawn from the experimental results 1 The proposed 3 DOF counterbalance mechanism can efficiently compensate the gravitational torques up to 95 in any configuration of a wall mounted roll pitch pitch joint structure 2 The maximum joint torques required at the roll pitch pitch joints are reduced by 74 64 and 45 respectively This reduction allows the use of 100 W and 50 W motors instead of 400 W and 200 W motors for the 6 DOF robot having 5 kg payload and 0 9 m reach without gravity compensation This substantial reduction in motor capacity lead to the decrease in manufacturing cost and the increase in energy efficiency of the robot arm RE