Eccentric universal joints for parallel kinematic machine tools: variants and kinematic transformations

In the 1990’s enhanced capabilities of parallel kinematic machine tools (PKM) regarding stiffness, motion accuracy and dynamics have been announced generously. Extensive research and development has been done in this area to date. Regarding this, the application range of PKMs is still small. Looking for reasons often yields inadequate motion accuracy as well as insufficient workspace. In either case the passive joints of the kinematic chains pose essential weak points. This article is about eccentric universal joints as an alternative approach that can avoid drawbacks of conventional universal joints and finally enhance the application range of PKMs. However, one of the consequences is a more complex and no longer unique kinematic transformation. This is significant in a control context, where iterative calculations should be avoided when possible due to real-time demands and the uniqueness of the solution has to be guaranteed in any case. Though the general inverse kinematic problem of industrial robots is identical, no generic closed-form (non-iterative) solution is known so far. But often closed-form as well as unique solutions are possible yet by considering particular features of the kinematic chain. In this paper after an introduction types of joint eccentricity are discussed and corresponding inverse kinematic transformations are derived with control purposes in mind.