# Kinematics, workspace and singularity analysis of a multi-mode parallel robot

## TL;DR

This paper analyzes the kinematics, workspace, and singularities of a reconfigurable 3-PRPiR parallel robot capable of changing operation modes through locking and releasing joints, supported by a prototype demonstration.

## Contribution

It provides detailed kinematic and workspace analysis of a multi-mode parallel robot with lockable joints, including inverse and forward kinematics for each mode.

## Key findings

- Identified workspace regions for each operation mode.
- Derived inverse and forward kinematics equations for all modes.
- Validated analysis with a physical prototype.

## Abstract

A family of reconfigurable parallel robots can change motion modes by passing through constraint singularities by locking and releasing some passive joints of the robot. This paper is about the kinematics, the workspace and singularity analysis of a 3-PRPiR parallel robot involving lockable Pi and R (revolute) joints. Here a Pi joint may act as a 1-DOF planar parallelogram if its lock-able P (prismatic) joint is locked or a 2-DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation modes to three 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation modes are dealt with in detail. The workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. A prototype built at Heriot-Watt University is used to illustrate the results of this work.