A Generalised Quaternion and Clifford Algebra Based Mathematical Methodology to Effect Multi-stage Reassembling Transformations in Parallel Robots

Sudharsan Thiruvengadam, Jei Shian Tan, Karol Miller

Research output: Contribution to journalArticle

Abstract

A robotic manipulator is a networked assemblage of kinematic pairs, mobile platform(s) and/or tool(s) that generate motion and forces at its end-effector. A manipulator’s theoretical dynamic, kinematic and workspace capabilities are governed by the design parameters (mass, geometry, dimensions, etc.) of its kinematic pairs and its architecture (number of limbs, degrees of freedom, actuation ability, etc.). By adjusting or changing the manipulator’s parameters (both architectural and kinematic pair-related), either from a design standpoint or physically, the robot undergoes what the authors broadly refer to as a ‘reassembling transformation’. By effecting reassembling transformations on a robot, we may generate desired changes in the workspace, kinematic and dynamic capabilities for a specific task manoeuvre. This work presents a novel methodology that marries quaternion rotors, the Lagrangian formulation, geometric algebra and associated mathematical apparatus, to tackle the problem of analysing and modelling robotic manipulators or mechanisms that undergo such ‘reassembling transformations’. Upon presenting a quaternion-based methodology for position, kinematics and Lagrangian dynamics, reassembling transformation types are introduced and detailed. We apply reassembling transformations to a Delta manipulator, in two separate case studies, each with unique target changes to the dynamic capabilities of the post transformed robot in its chosen task manoeuvres. The framework presented in this paper is generalised and its methods can be used to analyse and transform any parallel manipulator and also extended to the study of non-linear systems of equations for modelling multi-body dynamics.

Original languageEnglish
Article number39
JournalAdvances in Applied Clifford Algebras
Volume31
Issue number3
DOIs
Publication statusPublished - Jul 2021

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