Communication Tabulation of the Symbolic Midframe Jacobian of a Robot Manipulator

Abstract

The symbolic midframe Jacobian for a general 6-DOF ma-nipulator, a 12-DOF, 6-cylindric-jointed manipulator (6C) and a 24-DOF manipulator in which all four kinematic parameters of each link transform vary, admits to direct, manageable tabulation. For 6-link manipulators, the mid-frame Jacobians 3Jα and 3Jα associated with rates of change in the link lengths a and twists a do not depend upon the kinematic parameters of the first link frame (d1, &thetas;1, a,, α1). Similarly, the Jacobians 3Jd and 3J&thetas; associated with the rates of change in link offsets d and rotations &thetas; do not depend on the kinematic parameters of the sixth link frame (d6, &thetas;6, a6, α6). A general property of a manipulator Jacobian, ex-pressed in any frame, is that the column associated with the rate of change of a kinematic parameter is independent of that kinematic parameter. Furthermore, the determinant of the manipulator Jacobian is invariant with respect to its frame of representation, hence, the manipulator singularities may be calculated with relative ease in midframe. Finally, the complexity of the general form of 3Javersus 3Jd and 3Jα versus 3J&thetas;, as measured in types of symbols (+,-,., sines, cosines, parameters) and quantity of symbols of each type, is the same. 1

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oai:CiteSeerX.psu:10.1.1.987.6370Last time updated on 11/2/2017

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