INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 14, No. 1, pp. 61-68 JANUARY 2013 / 61 © KSPE and Springer 2013 Design of a Static Balancer with Space Mapping Chang-Hyun Cho 1 , Woo-Sub Lee 2,3 , and Sung-Chul Kang 2,# 1 Department of Control, Instruments, and Robot, Chosun University, 375 Seosuk-dong, Dong-gu, Gwang-ju, South Korea, 501-759 2 Center for Bionics, KIST, Hawolgok-dong, Sungbuk-gu, Seoul, South Korea, 136-791 3 Dept. of Mechanical and Aerospace Engineering, Tokyo Institute of Technology, Ishikawadai 1st bldg R510 (11-52), 2-12-1, Ohokayama, Meguro-ku, Tokyo, Japan, 152-8552 # Corresponding Author / E-mail: kasch804@gmail.com, TEL: +82-2-958-5589, FAX: +82-2-958-5629 KEYWORDS: Static balancing, Gravity compensation, Space mapping, Manipulator This paper proposes a general expression of the energy method for an n-dofs and n-links gravity compensator in the basis of space mapping. Joint space and gravity compensator space are determined and a mapping between the two spaces is considered. The mapping matrix is determined by mechanical constraints between two spaces. Potential energy in the joint space (i.e., the manipulator mass) and potential energy in the gravity compensator space (i.e., springs) are derived in generic forms. The design equation is obtained by partial differentiation of the potential energy in the both spaces and spring coefficients are determined with the design equation. Example studies are conducted to evaluate the mapping method. The bevel gravity compensator and a three-link spatial manipulator with the bevel gravity compensator are investigated. For the three-link spatial manipulator, the bevel gravity compensator and one-dof gravity compensator are equipped for link 3 and link 1 and the parallel constraint is adopted between the base and link 2 to obtain complete gravity compensation for all poses of the manipulator. Experimental results on gravity compensation indicate that gravitational torques are effectively counterbalanced. Manuscript received: March 21, 2012 / Accepted: August 2, 2012 1. Introduction Manipulators of a service robot are often operated at low velocity for safety reasons. In such a case gravitational or static torques are greater in value than dynamic torques. That is, torques generated by motors are wasted to compensate gravity for poses of a manipulator. To overcome this inefficiency caused by the static torques, gravity compensators are adopted to counterbalance the gravitation torques generated by the manipulator mass. 1 Gravity compensators with springs have been proposed over several decades. 2,3 A one-dof gravity compensator comprised of a pulley, wire and spring was proposed. 4 The profile of the pulley was modified to correspond to the rotation angle of a link to achieve complete gravity compensation. An internal cam device to counterbalance the gravitational torque was suggested and applied to a three-dof five-bar mechanism. 5 Endo et al. presented a five-bar mechanism with static balancer comprised of one-dof gravity compensators with non-circular pulley. 6 A three-dof gravity compensator for yaw-roll-pitch rotations with a single spring was proposed. 7 A roll-pitch gravity compensator using the bevel gears was proposed, in which the roll-pitch rotation is decoupled with the bevel gears and two one-dof gravity compensators in 3 were equipped at the bevel gears to achieve complete static balancing. 8 For the gravity compensation of a multi-link manipulator all displacements of joints should be considered, since COM (center of mass) varies with the configuration of the manipulator. To overcome this limitation caused by the complex rotations the parallel constraint is often applied to a distal link to deliver the rotation of the distal link to the base link. 3,6,9,10 A parallelogram is adopted and the pseudo parallelogram is suggested. 3,7,9 The rotation of the distal link is delivered to the base link with a parallelogram where a two-dof gravity compensator is attached. 10 Agrawal and Fattah proposed the hybrid strategy for an n-link manipulator. 11 In their research a parallelogram is adopted to represent COM and springs are equipped at the parallelogram. Hirose et al. proposed a gravity compensation mechanism so called the float arm V. 12 A common counter weight is utilized and the double pulleys are effective to minimize the counter weight. Gravity- compensated parallel mechanisms were designed adopting concepts of balance springs and counterweights. 13,14 A counter weight is adopted for machining. 15 To obtain the spring coefficient of a gravity compensator the total potential energy of springs and the manipulator mass is often investigated. 7-9,11,16,17 Streit and Gilmore proposed a design method considering the potential energy. 16 A design method of an n-spring balancer for a one-link system with two-dofs rotation was proposed, in which the spring parameters were derived by investigating the general DOI: 10.1007/s12541-013-0010-5