Full Forward Kinematics of Lower-Mobility Planar Parallel Continuum Robots

Abstract

In rigid lower-mobility parallel manipulators the motion of the end-effector is partially constrained due to a combination of passive kinematic pairs and rigid components. Translational mechanisms, such as the Delta manipulator, are the most common ones among this type of mechanisms. When flexible elements are introduced, as in Parallel Continuum Manipulators, the constraint is no longer rigid, and new challenges arise in performing certain motions depending on the degree of compliance. Mobility analysis shifts from being purely a geometric issue to one that heavily relies on force distribution within the mechanism. Simply converting classical lower-mobility rigid parallel mechanisms into Parallel Continuum Mechanisms may yield unexpected outcomes. This work, making use of a planar parallel continuum Delta manipulator, on the one hand, presents two different approaches to solve the Forward Kinematics of planar continuum manipulators, and, on the other hand, explores some challenges and issues in assessing the resultant workspace for different design alternatives of this kind of flexible manipulators.

Keywords

• continuum manipulators
• cosserat rods
• forward kinematics
• workspace
• quasi-translational motion
• parasitic angle