Sheth–Uicker convention revisited

•Review of kinematic conventions of last decades showing interconnections•Comparison of Denavit–Hartenberg and Sheth–Uicker convention•Unified notation using frame sets•Kinematic conventions and their line-geometric background•Comparison of Dual Euler Angle representation and Finite Twist representation

In this article, different conventions for specifying kinematics of mechanisms and their properties are reviewed with emphasis on the convention developed by Sheth and Uicker in 1971. This convention partitions displacements in joint and link displacements and decomposes these displacements into three axial screw displacements. Because of this systematic construction, the convention features several practical and theoretical preferences which are reflected in this article. To do so, two comparisons are made: first, the Sheth–Uicker convention is compared to other kinematic conventions. Second, the convention – as the Dual Euler Angle representation of finite spatial displacements – is placed into the context of three other popular displacement representations. To enable these comparisons in a consistent manner, notations of necessary entities are assembled, adapted, or newly defined. In general, this article is intended as a contribution to the development of a commonly accepted normal form for kinematics of mechanisms.