Jacobian inversion analysis and extraction of dexterous workspace in PKMs

Abstract

The emerging interest in the use of parallel kinematic machines for machining applications requires extensive research to determine proper workspace and dexterity when designing PKMs. Theoretically, the jacobian matrix is used to calculate all the performance parameters in PKMs. The condition number plays the role of an observer calculated for every point of the workspace in order to identify the location's reachability and dexterity. The paper discusses issues related to the Jacobian inversion to determine the dexterity space. A program has been made to analyse the extraction of dexterity from workspace with two examples to illustrate this. Issues concerning dexterity and the jacobian inversion are also discussed.