A Weight Compensation Mechanism with a Non-Circular Pulley and a Spring: Application to a Parallel Four-Bar Linkage Arm

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1 SICE Journal of Control, Measurement, and System Integration, Vol. 3, No. 2, pp , March 2010 A Weight Compensation Mechanism with a Non-Circular Pulley and a Spring: Application to a Parallel Four-Bar Linkage Arm Gen ENDO, Hiroya YAMADA, Akira YAJIMA, Masaru OGATA, and Shigeo HIROSE Abstract : We propose a new weight compensation mechanism with a non-circular pulley and a spring. We show the basic principle and a numerical design method to derive the shape of the non-circular pulley. After demonstration of the weight compensation for an inverted pendulum system, we extend the same mechanism to a 2 degrees of freedom (DOF) parallel four-bar linkage system, analyzing the required torques with transposed Jacobian matrices. Finally, we develop a 3-DOF manipulator with relatively small output actuator and verifies that the weight compensation mechanism significantly contributes to decrease static torques to keep the same posture within manipulator s work space, which is also effective in a dynamic movement. Key Words : weight compensation mechanism, balancer, parallel four-bar linkage. 1. Introduction A serial link arm with revolute joints requires a large torque to compensate its own gravity especially for the base actuator due to the serially connected linear configuration. Installing a large actuator to generate the compensation torque is not energy efficient because the actuator power is merely used to keep the static balance and not used for external work. Moreover, equipping with large actuators may lead to a negative spiral because large actuators are usually heavy and installing heavy actuators increases the total weight of the arm which consequently generates a more gravity torque. Therefore a passive weight compensation mechanism (WCM) is desirable to achieve a high performance and energy efficiency for various tasks. Figure 1 shows typical examples of passive WCMs for a 1 degree of freedom (DOF) inverted pendulum system. There is a spring between the base link and rotating arm link, and the gravity torque depending on the link posture θ is canceled by the spring force in Figs. 1(a) and (b). This simple mechanism is widely used for industrial robots in terms of energy efficiency because this mechanism significantly reduces the maximum gravity torque. Additionally the spring-suspended configuration is also preferable in terms of safety because the mechanism prevent the link from a rapid falling in case of a power shutdown. (Note that configurations in Figs. 1(a) and (b) can be analyzed by the same kinematic model. However, that in Fig. 1(b) recently becomes more popular due to the large workspace and small width.) However, Figs. 1(a) and (b) with an ordinary linear spring can not perfectly compensate the gravity torque within the link s workspace because the mechanism requires an ideal linear spring whose natural length is zero to compensate the gravity torque regardless of the link posture θ [1]. To solve this problem, Rahman et al. [2] proposed a new configuration where a spring is installed within the link and the end of the spring is connected to the base link using a wire-pulley mechanism. This configuration virtually equals to the ideal spring (Fig. 1(c)). (The same mechanism is also proposed by Morita et al. [3]) However a linear spring generating sufficient compensation force tends to be large and the material of the spring is usually heavy steel. Thus this mechanism may increase the total weight of the arm. Figure 1(d) has a counter-weight at the end of the link to compensate the weight of theend effector. This mechanism can keep the center of gravity on the joint axis and thus the moment of the gravity force of the base link is always zero regardless of θ. This configuration is suitable for an application where the base link can not be rigidly fixed to the ground [4]. On the other hand, the moment of inertia increases due to the additional weight for the counter balance. Therefore it is not appropriate for a rapid movement with large acceleration and deceleration. Based on the previous works, we adopt the most popular configuration illustrated by Fig. 1(b) and propose to install a noncircular pulley rotating with the arm link to perfectly balance within arm s workspace [5]. There are several former works to appropriately adjust the spring force/torque profile by a non-circular pulley. Okada proposed a pantagraphic mechanism with non-circular pulleys and springs for an inner pipe inspection mobile robot to generate constant pushing force of driving wheels against various diameter pipes [6]. Ulrich et al. developed a WCM with non-circular Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology, I1-60, Ookayama, Meguro-ku, Tokyo , Japan Canon Inc., 70-1, Yanagi-cho, Saiwai-ku, Kawasaki-shi, Kanagawa , Japan gendo@mes.titech.ac.jp (Received September 8, 2009) Fig. 1 Conventional weight compensation mechanism. JCMSI 0002/10/ c 2009 SICE

2 SICE JCMSI, Vol. 3, No. 2, March pulleys and parallel antagonistic linear springs for a serial link 2-DOF system [7]. However, these previous works still remain a laboratory experiment level because they required many assumptions to analytically derive the shape of the non-circular pulley, which is not preferable for a practical design. In the reference [8], non-circular gears and circular pulleys are incorporated to a WCM. However the mechanism requires many mechanical parts and they are rather complicated and bulky. In this paper, we propose a numerical design method to derive the shape of the non-circular pulley which is more practical and applicable to the various industrial robots. We develop a parallel 4-bar linkage arm with active joints and apply the WCM. We demonstrate that the WCM remarkably contributes to decrease static torques to keep the same posture within the manipulator s workspace by hardware verifications. In Section 2, we explain the basic principle of the weight compensation with a non-circular pulley and a spring, and describe numerical design procedures for the non-circular pulley. Then we verify the effectiveness with a passive 1-DOF pendulum system. In Section 3, we extend the mechanism to 2- DOF 4-bar parallel link system analyzing the gravity torques with transposed Jacobian matrices. We develop a parallel 4- bar linkage arm with active joints with a WCM and experimentally show that the proposed mechanism significantly decreases static torques. Finally we conclude this paper in Section Weight Compensation Mechanism with a Non- Circular Pulley and a Spring 2.1 Basic Principle In this section, we discuss the basic principle of the weight compensation mechanism for an 1-DOF pendulum system (Fig. 2). The arm link with the end-mass freely rotates to the base link. The non-circular pulley is fixed to the arm link. One extremity of the spring is connected to the base link and the other extremity is connected to the flexible part without elongation such as a wire or a belt. The extremity of the flexible part is fixed to the pulley and the flexible part is twisted around the non-circular pulley. Therefore arm link rotation winds the flexible part and the stretched spring generates the compensation torque whose magnitude equals to the spring force multiplied by the diameter of the non-circular pulley. We define θ = 0 when the arm is perfectly inverted and describe it inverted pendulum (0 θ π/2) or ordinary pendulum (π/2 θ π) as a matter of convenience. If we can design pulley radius r(θ) satisfying the following identity of θ, the system becomes totally balanced system with zero gravity. F s r(θ) = Mgl sin θ, (1) where F s is spring force and M, g, l are the weight of the end mass, gravity acceleration and link length, respectively. This mechanism is composed of only three parts (noncircular pulley, flexible part and spring) and very simple structure. And additional moment of inertia can be minimized with the high stiffness spring and small diameter non-circular pulley. Moreover, we can set arbitrary torque profile τ(θ) in the right-hand side of Eq. (1). F s r(θ) = τ(θ). (2) We can set different torque profile depending on the application. For example, the arm generates lifting force of mg/4 when θ = π/2. This means that the mechanism is not limited to the weight compensation only and applicable to the various mechanism design. In summary, this mechanism has following advantages: 1) wide range and precise weight compensation, 2) minimum increase of moment of inertia, 3) arbitrary torque profile for various application. 2.2 Numerical Design Method for a Non-Circular Pulley In the reference [7], two linear springs were arranged in parallel acting in an opposing manner to drive pulley. This configuration was introduced to mathematically derive the shape of the pulley. As a result, the total size of the mechanism was not compact enough for a practical application. In this paper, we derive the shape of the pulley by using the numerical iteration which is less constraints and more applicable compared with the previous analytical approaches. The proposed algorithm is based on the reference [9] which was used for adjusting a joint torque profile using a Shape Memory Array (SMA) actuator. We extended the algorithm to set various torque profile. The designing procedure is as follows: 1. Set structural design parameters a, b in Fig. 3, as well as initial arm angle θ 0 and desired torque profile τ(θ). 2. Set spring stiffness k, natural length x 0, initial tension F 0. In case of an ordinary linear spring, spring force F s can be expressed as F s = kx + F 0,wherex is displacement. 3. Numerical design starts with maximum displacement x max of the spring, where initial pulley radius is r 0 = τ(θ 0 )/F max. Fig. 2 Weight compensation mechanism with a non-circular pulley and a spring. Fig. 3 Procedure to derive the non-circular pulley.

3 132 SICE JCMSI, Vol. 3, No. 2, March Draw a tangent line of a circle l 0 to intersect the fixed point of the spring P 0 in Fig. 3, where the center of the circle is O and its radius is r 0.DefineC 0 which is intersection of l 0 and X axis. 5. Draw a circle with radius of OP 0 and define points P 1, P 2,...,P n with constant incremental angle Δθ in the motion range (θ 0 θ θ max ). This is because an analytical procedure is to be taken in which the pulley curve is drawn around the rotating center O by inversely rotating the spring supporting point P i (instead of rotating the pulley) and unwinding the flexible part at the spring end from the pulley side. Fig. 4 Non-circular Pulley for an inverted pendulum. 6. Choose a random point α on the tangent line l 0. Obtain the displacement x α of the spring stretched between the segment αp 1 and distance r α of the straight line αp 1 from the origin O. The variation of the displacement of the spring stretched from the point α is (αp 0 αp 1 ) because the flexible part wound around the pulley is supposed to be non-ductile. Consequently, the displacement is x α = x max (αp 0 αp 1 ), where spring force is F sα = k x α + F 0. Fig. 5 Experimental results of weight compensation for 1-DOF inverted pendulum system. 7. Perform the operation in which the position of the point α is shifted until it agrees with the desired torque profile τ(θ) by F sα r α by means of a convergent calculation. 8. Make the position of α the point C 1, which is the first vertex of the pulley configuration to be polygonally approximated. 9. Assume a new point α on the straight line C 1 P 1 and repeat the calculations of for the points α and P 2 to obtain C Repeat the above-mentioned procedure until the displacement becomes zero or θ = θ max. In above example, we select a linear spring with initial tension but we can select any kind of spring including non-linear property. And the numerical design proceed in unwinding direction (Δθ 0) in this example but opposite winding direction (Δθ 0) is also possible. (Note that the initial displacement becomes minimum displacement in this case.) This numerical method does not guarantee the convergence of the shape of the pulley. Thus, the pulley shape may diverge or converge to extremely large radius depending on the initial parameter sets. On the other hand, this algorithm requires less constraints compared with analytical method and permits the designer to test various combination of springs and structural parameters which is appropriate for a practical design. The calculation time is less than 1sec with Intel Core2 Quad CPU 3GHz. Therefore we consider this algorithm as sufficiently practical method even if the designer has to search by trial and error. 2.3 Verification Experiment for 1-DOF Pendulum System To verify the proposed mechanism with numerical design method, we carry out weight compensation experiments for 1-DOF inverted pendulum shown in Fig. 2. The non-circular pulley is designed on condition that the end mass is 0.5kg, the lengthofthelinkis0.5m, Δθ = 0.5deg and the diameter of the wire winded around the pulley is assumed to be negligible small. We choose a tension coil spring made of stainless steel (MISUMI Group Inc.: AUFM12-100, k = 1.15N/mm, F 0 = 14.71N, x max = 75.21mm). The weight compensated range of motion is maximized by manually adjusting structural parameters by trial and error. Derived non-circular pulleys for the inverted pendulum is shown in Fig. 4. The shapes of the edges of the non-circular pulley which are not related to the weight compensation are arbitrary designed. The non-circular pulley was manufactured by a CNC milling machine and the theoretical range of weight compensation is 18 90deg. The arm link can ideally keep any posture within these range of motion. Figure 5 illustrates joint torque measured by a spring balance. We adjusted the vertical position of the spring end fixed to the base structure to minimize the compensation error. The arm could not always keep the same posture regardless of θ due to hardware error such as the elongation of wire, the effect of the diameter of the wire and deviation of spring stiffness. However Fig. 5 clearly shows that the maximum joint torque with the weight compensation is less than 10 % of the theoretical gravity torque without weight compensation. We also verified the effectiveness of reducing the maximum joint torque for an ordinary pendulum [5]. 3. Application to a Parallel 4-Bar Linkage Arm In this section, we discuss a WCM for a parallel 4-bar linkage arm shown in Fig. 6. Two actuators are installed at the origin O and drive Link 1 and Link 2, independently. This configuration is often adopted by industrial robots because heavy actuators can be mounted on the base link that contributes to decrease moment of inertia of the arm. It is very important to discuss a concrete application of the WCM for a practical design. 3.1 Analysis of Gravity Torques It is generally known that a parallel 4-bar linkage has a decoupled structure where the gravity torque independently act on each joint [10]. To analytically obtain gravity torques, the arm is modeled as 6 point mass including the end mass and

4 SICE JCMSI, Vol. 3, No. 2, March Fig. 6 Kinematic model of a parallel four-bar linkage arm with 2-DOF actuation. Fig. 7 Prototype model of a parallel four-bar linkage arm for a light duty operation (version 2). the weight of the links (Fig. 6). The joint torque vector τ i due to the point mass m i is obtained by the inner product of the transposed Jacobian matrix J T i (θ) for the position of m i and the gravitational force vector regarded as the external force F i = (0, m i g). By summing the joint torque vectors due to each mass point as τ = (τ 1,τ 2 ) T = i JT i (θ) F i, we can acquire the following solution. ( ) τ1 {m 1 l 1 + m 3 l 3 + (m 4 + m 5 + m 6 )l a }g sin θ 1 = τ 2 {m 2 l 2 + m 3 l b + m 4 l 4 m 5 l 5 m 6 l a }g sin θ. (3) 2 The Eq. (3) analytically proves that τ 1 depends on only θ 1, and θ 2 never affects on τ 1. Thus, we can directly apply the designing procedure for 1-DOF system described in Section 2 to the 2-DOF parallel 4-bar linkage arm. 3.2 Light Duty Light Weight Arm We have developed a 3-DOF light weight arm for a pick & place task for an assembly of an electric device. In this section, we describe outlines of the arm. We plan to report the detailed design and its specification in the next paper. When we think about a design of the arm where the arm and a human worker share the same narrow working space such as a cellular manufacturing system, the weight of the arm and its output power should be as small as possible in terms of safety. Moreover Japanese Industrial Standards prohibit sharing the work area without barriers if a human worker works with the industrial robot which has more than 80w for each driving joint [11]. Therefore we decided to use CFRP pipes for the links to reduce the weight of the arm structure and arranged actuators to be concentrated on the base link to reduce the moment of inertia of the arm. Moreover we installed the above-mentioned WCM to reduce static gravity torque which permits the small actuator to sustain any static posture. Figure 7 shows the overview of the developed arm. To construct 3-DOF polar coordinate system, a swivel degree of freedom around the vertical axis is introduced to the 2-DOF parallel 4-bar linkage arm as a base link. The actuator output power is only 20w which permits a human worker to share the same working space with the arm. For the arm structure, we developed two prototype models denoted as version 1 and 2. The first prototype version 1 was constructed by CFRP pipes of 4mm thickness in order to ensure sufficient rigidity. As a result, the total weight of the upper arm Table 1 Specification of the arm. Arm Length mm 500(Link 1)+500(Link 2 ) Maximum Reach mm R=985 J 0 : θ 0 = ±90 Range of Motion deg J 1 : θ 1 = 0, 90 (where θ 1 θ 2 > 20) J 2 : θ 2 = -90,0(whereθ 1 θ 2 < 160) Actuator Maxon RE25 (20W) * 3 Payload kg 0.5 Total Weight kg 4.5 which was driven by J 1 and J 2 actuators was 1.677kg,whichis still heavy. To reduce the total weight of the arm furthermore, the second prototype version 2 used CFRP pipes of 1mm thickness. Additionally, we introduced mechanical limits to prevent the links from interference and electrical limit switches to detect initial zero position for incremental encoders for the safe and ease of operation. Despite installing additional mechanical parts, version 2 was successfully reduced 25% of the total weight to 1.264kg. Table 1 shows the specification of the prototype model version 2. The developed arm is extremely light weight compared with a commercially available industrial robot with the same arm length such as the reference [12] (35kg). 3.3 Design of the Weight Compensation Mechanism J 1 and J 2 joint have the same driving mechanism. Figure 8 shows the detailed mechanism for J 1. The actuator output torque is transmitted by a timing-belt to the input shaft of the harmonic reduction gear unit. The output of the harmonic unit drives the non-circular pulley fixed to the link structure. The non-circular pulley winds the steal belt and stretch the spring to generate compensation torque. We adopt a steel belt instead of using a wire to improve the accuracy of the weight compensation. Because the steel belt has very thin (0.1mm thickness) and negligible small elongation with sufficient strength. Note that the joint stiffness does not essentially decrease by introducing the spring because the spring is connected parallel to the joint actuation. The shape of the non-circular pulley highly depends on the mass property of the arm. We show two examples of the noncircular pulley design. Table 2 shows the mass property data acquired by 3D CAD model. The weight compensation torques for each joint are calculated by mass property data and Eq. (3). The gravity torque for each joint can be come down to a virtual 1-DOF pendulum system. Here, we assume the link length of

5 134 SICE JCMSI, Vol. 3, No. 2, March 2010 Fig. 10 τ 1 without compensation. Fig. 8 Joint diving mechanism with the non-circular pulleys and the springs. Table 2 Mass property data of prototype version 1 and version2. Mass kg m 1 m 2 m 3 m 4 m 5 m 6 mi Ver Ver Length m l 1 l 2 l 3 l 4 l 5 l a l b Ver Ver Fig. 11 τ 1 with compensation. Fig. 9 Derived shape of the non-circular pulleys with different mass properties. Fig. 12 τ 2 without compensation. 0.5m for the simulated equivalent pendulum. The gravity torque τ 1 for version 1 and 2 are equivalent to an inverted pendulum with the end mass of 1.183kg, 0.858kg, respectively. Similarly, τ 2 for version 1 and 2 are equivalent to an ordinary pendulum with the end mass of 0.330kg, 0.302kg, respectively. The end mass of version 2 is smaller than that of version 1 because of the reduced weight of the arm. Moreover, τ 1 is much larger than τ 2 because actual length of the link1 is larger than that of link 2. Figure 9 shows derived shape of the non-circular pulleys based on mass property analysis. The size of the non-circular pulley for version 2 is smaller than version 1 due to less weight of the arm structure, which consequently leads to the smaller compensation torque. The results indicates that proposed algorithm successfully derive appropriate shapes of the non-circular pulley depending on the mass property of the arm. Theoretical ranges of the weight compensation in deg for version 2 are 14.0 θ and 90.0 θ Two parallel springs are incorporated for J 1 compensation due to the high gravity torque. The specifications of the spring are x 0 = 80mm, x max = 55.85mm k = 1.33N/mm and F 0 = 12.4N (MISUMI Group Inc.: AWFM10-80). Fig. 13 τ 2 with compensation. 3.4 Experiment Static torque measurement To quantify the reduction of the joint torque to keep a static posture, we measure the absolute value of current for each actuator when the arm takes grid-points in 0.1m distance in absolute coordinate system. For each grid-points, the arm keeps the same posture for a few seconds and the torque is calculated by the actuator current measured by a local motor driver (Maxon: EPOS24/5) and torque constant 43.8mNm/A of the actuator. The measurement accuracy is about ±1mNm since the measured torque includes frictional torque of the harmonic drive unit. Figures 10 and 11 indicate the torque difference of J 1 between without or with the WCM. Figures 12 and 13 are comparison for J 2. The fan-shaped boundaries show arm s

6 SICE JCMSI, Vol. 3, No. 2, March Fig. 14 J 1 current (period:1.2sec). Fig. 16 J 2 current (period:1.2sec). Fig. 15 J 1 current (period:19.2sec). Fig. 17 J 2 current (period:19.2sec). workspace and contour lines are drawn by every 5mNm. The maximum gravity torque for J 1, which has the longer link length, is 45.6mNm without the WCM (Fig. 10). Since the maximum continuous torque of the actuator from specification in data sheet is only 26.7mNm, the installed actuator can statically sustain the posture less than in a half of the workspace. On the contrary with the WCM, required maximum torque is drastically decreased to 11.7mNm which is 74% off (Fig. 11). Thus it is possible for the installed small actuator to sustain any posture within arm s workspace. In the same way, Figs. 12 and 13 show that the maximum torque on J 2 decreases from 17.3mNm to 8.2mNm which is 50% off. Therefore we could conclude that the proposed weight compensation mechanism is quite effective to reduce required torque to keep static posture with small actuators Dynamic torque measurement Next we evaluate required torques in a dynamic movement. It is impossible for the WCM to compensate a dynamic torque due to acceleration and deceleration. However, it is supposed that the arm with the WCM achieves faster movement because required total joint torque is decreased by cancelling the static gravity torque. To verify the effectiveness of introducing the weight compensation mechanism in a dynamic movement, we measured current on the joint actuator during a standard cycle. 1 The initial and terminal position of the standard cycle are set to (x, z) = (500, 0) and (x, z) = (800, 0), respectively. The currents with or without the WCM were measured by 12msec in average during the standard cycle movement at cycle times of 1.2sec and 19.2sec, respectively. In our case, introducing the WCM did not cause any side effect such as vibration of the system due to the resonance in the range of achievable cycle time. Figures show the results of current measurements. The time in horizontal axis is normalized by its cycle period to evaluate dynamic effect on joint torques. Solid bold and thin 1 The standard cycle is a reciprocal motion composed of the height elevation of 25mm, the horizontal movement of 300mm and the height declination of 25mm in series. The cycle is often used to evaluate manipulator s performance in industrial robots. lines indicate measured current with or without the WCM, respectively and dashed lines are desired joint angles. By comparing Fig. 14 with Fig. 15, shorter cycle period (1.2sec) requires larger current than that of quasi-static movement (19.2sec). The difference suggests an effect of dynamics because the joint trajectory is identical in both experiments except for its cycle period. Meanwhile we can observe that current profile without the WCM has an negative offset in the Y direction compared with the current introducing the WCM. And absolute peak current without the WCM is much higher than with the WCM. This current offset suggests an effect of static gravity torque. The similar tendency is also observed in J 2 current although the difference with/without the WCM is not so large due to shorter link length. These results suggest that the WCM removes the current offset due to gravity torque. This effect has three advantages. The first advantage is to decrease the maximum value of absolute current. It is preferable for the robot to perform a movement with low current in terms of energy efficiency. With the WCM, all actuator current supplied by a motor driver is consumed by a purely dynamic movement. Thus, the robot with the WCM can performs more agile movement than the robot without the WCM, consuming the same amount of actuator current. Moreover, it is preferable to drive the robot with a low current capacity motor driver which is cost effective in practice. The second advantage is to remove an unidirectional load for a driving joint. The current offset generates unidirectional torque to the driving mechanism. Generally, directional load is not preferable for a driving mechanism because it reduces endurance time. 2 By introducing the WCM, joint driving torque equals to dynamic torque due to acceleration and deceleration, which is essentially isotropic. Therefore the WCM is advantageous in terms of mechanical endurance. The third advantage is to increase setpoint tracking accuracy. It is generally known that PD control with gravity compensation in control theory has better set-point tracking performance than without gravity compensation [13]. 2 Actually, the harmonic drive gear head is not recommended in unidirectional load in its data sheet.

7 136 SICE JCMSI, Vol. 3, No. 2, March 2010 The WCM offers the same effect without requiring feed forward torque which consumes more energy. These results suggest that introducing the WCM is also beneficial for the arm robot even in dynamic movements. 4. Conclusion In this paper, we have discussed a passive weight compensation mechanism (WCM) with a non-circular pulley and a spring. We proposed a numerical design method to derive the shape of the pulley which is with less restrictive constraints and more applicable compared with the previous analytical approaches. After preliminary verifications of the designing method for a single pendulum system, we have extended the WCM to a 2-DOF parallel 4-bar linkage arm, analyzing the gravity torques with transposed Jacobian matrices. Finally we have quantitatively investigated the effectiveness of the reduction of the required torque by measuring the actuator current of the light duty light weight arm. Introduction of the WCM significantly reduces the maximum static torque by 50-80% to sustain static posture. Moreover the WCM contributes to remove a torque offset due to the static torque even in a dynamic movement, which is also effective to decrease the peak of the absolute value of current. Currently the WCM does not have an adjusting mechanism for the different end effector which is far different from the designed weight. Introducing the adjusting mechanism as in the reference [14] remains as one of our important future works. Moreover, we have determined the designing parameters, such as the spring stiffness and initial radius of the non-circular pulley etc., through a trial and error process in this paper. Thus the derived shape of the non-circular pulley has not been fully optimized yet. Using an optimization method such as genetic algorithm also forms one of our future works. References [1] S. Hirose and H. Kuwahara: Basic study on gravity compensated multi joint arm, Proc. 12th Annual Conf. of the Robotics Society of Japan, pp , 1994 (in Japanese). [2] T. Rahman, R. Ramanathan, R. Seliktar, and W. Harwin: A simple technique to passively gravity-balance articulated mechanism, ASME Transactions on Mechanisms Design, Vol. 117, No. 4, pp , [3] T. Morita, F. Kuribara, Y. Shiozawa, and S. Sugano: A novel mechanism design for gravity compensation in three dimensional space, Proc. Int. Conf. Advanced Intelligent Mechatronics (AIM03), pp , [4] Y. Tojo, P. Debenest, E. F. Fukushima, and S. Hirose: Robotic system for humanitarian demining development of weight-compensated pantograph manipulator, Proc. Int. Conf. Robotics and Automation, pp , [5] G. Endo and S. Hirose: A weight compensation mechanism with a non-circular pulley and a spring: Application to a parallel link manipulator, JSME Annual Conference on Robotics and Mechatronics, 1A1-G20, 2008 (in Japanese). [6] T. Okada and T. Kanade: A three-wheeled self-adjusting vehicle in a pipe, FERRET-1, International Journal of Robotics Research, Vol. 6, No. 4, pp , [7] N. Ulrich and V. Kumar: Passive mechanical gravity compensation for robot manipulators, Proc. Int. Conf. Robotics and Automation, pp , [8] S. L. Chow and C. F. Shi: Passive gravity-compensating mechanism, United States Patent: B2, [9] S. Hirose, K. Ikuta, and K. Sato: Development of shape memory alloy actuator: Improvement of output performance by the introduction of a σ-mechanism, Advanced Robotics, Vol. 3, No. 2, pp , [10] M. W. Spong and M. Vidyasagar: Robot Dynamics and Control, Wiley, [11] Japanese Industrial Standards: Robots for industrial environments Safety requirements Part 1: Robot, JIS B :2007. [12] DENSO WAVE INCORPORATED: Industrial Robots 5- and 6- Axis Robots: VS-G Series[Specifications], spec-ja.html [13] F. L. Lewis, D. M. Dawson, and C. T. Abdallah: Robot Manipulator Control, Marcel Dekker Inc., [14] H. Sekiguchi and T. Nishimura: Robot, United States Patent: , Gen ENDO (Member) He received his B.S., M.S., and Ph.D. degrees from Tokyo Institute of Technology, Japan, in 1996, 1998, and 2000, respectively. From 2000 to 2007, he was with Sony Corporation and worked in Advanced Telecommunication Research Institute, International as a visiting researcher. He joined the Faculty of Tokyo Institute of Technology in 2007, where he is currently an Assistant Professor of Department of Mechano-Aerospace Engineering. Hiroya YAMADA He received his M.S. and Ph.D. degrees from Tokyo Institute of Technology, Japan, in 2005 and 2008, respectively. He joined the Faculty of Tokyo Institute of Technology, where he is currently a Tenure Track Assistant Professor of Global Edge Institute. His research interests lie in the area of biologically inspired robots. Akira YAJIMA He received his B.S. and M.S. degrees from Tokyo Institute of Technology, Japan, in 2002 and 2004, respectively. He joined Olympus Corporation and moved to Olympus Medical Systems Corporation in He joined Canon Inc. in He is working on research and development of a lightweight manipulator. Masaru OGATA He received his B.S., M.S., and Ph.D. degrees from Tokyo Institute of Technology, Japan, in 2000, 2002, and 2005, respectively. He joined the 21st century COE program in Tokyo Institute of Technology as a researcher in He joined Canon Inc. in His research interests include mechanism design and quadruped walking robots. Shigeo HIROSE (Member) He received his doctoral degree in control engineering from Tokyo Institute of Technology in He is a Fellow of the IEEE. His research interests include design and control of snake-like robots, walking robots, wheels and crawler vehicles, omnidirectional robots, wall climbing robots, planetary exploration robots, and devices for control of robots. He received the Pioneer in Robotics and Automation Award from the IEEE Robotics and Automation Society in 1999.