Kinematic Analysis of a Serial - Parallel Machine Tool: the VERNE machine

TL;DR

This paper derives the kinematic equations for the VERNE machine, a complex 5-axis serial-parallel machine, using symbolic methods to identify all solutions and constraints for its over-constrained parallel module.

Contribution

It introduces a symbolic approach to derive and analyze the kinematic solutions of a complex serial-parallel machine tool, including constraints for solution validity.

Findings

Derived inverse and forward kinematic equations for the VERNE machine.

Identified all kinematic solutions and constraints for the over-constrained parallel module.

Provided a method to select acceptable solutions based on analytical constraints.

Abstract

The paper derives the inverse and the forward kinematic equations of a serial - parallel 5-axis machine tool: the VERNE machine. This machine is composed of a three-degree-of-freedom (DOF) parallel module and a two-DOF serial tilting table. The parallel module consists of a moving platform that is connected to a fixed base by three non-identical legs. These legs are connected in a way that the combined effects of the three legs lead to an over-constrained mechanism with complex motion. This motion is defined as a simultaneous combination of rotation and translation. In this paper we propose symbolical methods that able to calculate all kinematic solutions and identify the acceptable one by adding analytical constraint on the disposition of legs of the parallel module.