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Modular Relative Jacobian for Combined 3-Arm Parallel Manipulators

Rodrigo S. Jamisola Jr. 1, Carlos Mastalli 2, and Frank Ibikunle 1
1. Electrical, Computer, and Telecommunications Engineering Dept., Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana 10071
2. Advanced Robotics Dept., Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy

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