Computational kinematics for robotic manipulators: Jacobian problems

Abstract

Purpose This paper aims to provide tools for the complete Jacobian analysis of robotic manipulators of general topology, using a comprehensive velocity equation. Design/methodology/approach First, a modelling process is made in order to build the velocity equation using simple constraint equations: i.e. length restriction, relative motion and rigid body constraints. Then the motion space is solved, i.e. the space that spans all feasible motions of the manipulator. Findings The velocity equation is comprehensive, i.e. it relates all kinematic variables, not only input and output. The Jacobian related to the comprehensive velocity equation is a square dimensionless matrix. This characteristic has great importance when evaluating manipulability or closeness to singularities. Employing the motion space, any kinematic entity can be studied: i.e. velocities and accelerations of any active/passive joints, screw axis, axodes, and so on. Also a comprehensive singularity analysis can be made. Research limitations/implications The approach presented is focused on the kinetostatic analysis of manipulators and, therefore, subjected to rigid body assumption. Practical implications The paper presents a proposal of effective codes for engineering analysis of manipulators. Originality/value This approach is based on a pure computational kinematic analysis that unifies all kinetostatic analysis for any manipulator topology (i.e. serial, parallel, hybrid manipulators, complex mechanisms, redundant‐or non‐redundant‐actuated). The characteristic Jacobian matrix is dimensionless and provides the means for a complete singularity analysis and an effective use of indicators.