Abstract—This work presents a new formulation of a modular relative Jacobian used to control combined manipulators as a single manipulator with a single effector. In particular, this modular relative Jacobian is designed for 3-arm parallel manipulators. It is called a relative Jacobian because it is expressed relative to the reference frames at the manipulator end-effectors. It is modular because it uses the existing information of each standalone manipulator component to arrive at the necessary expressions for the combined system. This work is part of a series of studies to express a single end-effector control of combined manipulators, in parallel as well as other types of base configurations. This holistic approach of controlling combined manipulators affords a drastic increase of the null-space dimension and the convenience to use all the principles of controlling a single manipulator for the resulting combined system. Derivation of the modular relative Jacobian for a 3-arm parallel manipulator is shown, together will simulation results. 

Index Terms—modular kinematics, 3-arm parallel manipulators, single end-effector control, relative jacobian

Cite: Rodrigo S. Jamisola Jr., Carlos Mastalli, and Frank Ibikunle, "Modular Relative Jacobian for Combined 3-Arm Parallel Manipulators," International Journal of Mechanical Engineering and Robotics Research, Vol. 5, No. 2, pp. 90-95, April 2016. DOI: 10.18178/ijmerr.5.2.90-95