The Adjoint Trigonometric Representation of Displacements and a Closed-Form Solution to the IKP of General 3C Chains

TitleThe Adjoint Trigonometric Representation of Displacements and a Closed-Form Solution to the IKP of General 3C Chains
Publication TypeJournal Article
Year of Publication2020
AuthorsBongardt B
JournalJournal of Applied Mathematics and Mechanics
Date Published05/2020
Abstract

Based on the representation of rigid body displacements as adjoint matrices, the article introduces the adjoint trigonometric representation of displacements (ATRD) as a further generalization of the trigonometric representation of rotations. In comparison to the dual Rodrigues–Euler–Gauß–Gelman equation, recently reported for affine screw displacements with arbitrary, fixed pitches, the ATRD is built upon a product of a unit line and a dual angle, instead of upon a product of a unit screw and a real angle. Due to this conceptual difference, the ATRD requires four independent parameters of a unit line instead of five when parametrizing a displacement along a unit screw. As a consequence for computational kinematics, the ATRD permits transferring the analytic solution to the inverse kinematics problem (IKP) of 3-DOF, general, spherical 3R-chains into a closed-form solution to the IKP of 6-DOF, general, affine 3C-chains.

URLhttps://onlinelibrary.wiley.com/doi/epdf/10.1002/zamm.201900214
DOI10.1002/zamm.201900214