Automatic Computation for Robot Design (ACRoD): A Python package for numerical calculation of Jacobian of a robot at a given configuration around a specified end-effector point

Abstract

The Jacobian of a robot refers to the matrix that linearly maps the velocity components of the end-effector and the velocities at the actuated joints. The Jacobian is extensively used in dimensional synthesis for Jacobian-based optimal performances of robotic manipulators, in which the optimal dimensional parameters of robots are computed. Determination of accurate mobility (Yang et al., 2008) of planar and spatial mechanisms can also be performed by using Jacobian in cases where Chebychev–Grübler–Kutzbach criterion cannot accurately determine the mobility (Gogu, 2005). As a result, Jacobian is a significant part for both kinematic analysis, dimensional synthesis and mobility determination of a mechanism. Hence, the formulation of Jacobian has its key importance in the literature and in the application of performance optimisation along with mobility computation. Formulation of Jacobian for serial manipulators can be computed easily, however, it is increasingly complicated to formulate Jacobian for parallel manipulators due to the existence of passive joint velocities and the nature in which these are related to active joint velocities. Several studies (Altuzarra et al., 2006; Dutre et al., 1997; D. Kim et al., 2000; S.-G. Kim &