Kinematic Analysis of three degrees of freedom planar parallel continuum mechanisms

Parallel continuum mechanisms are a type of compliant mechanisms comprising a rigid end-effector connected to a fixed frame by flexible and slender elements in a closed-kinematic morphology, being their flexibility the source of mobility. Solving the position problem involves the static equilibrium of the whole device considering the nonlinear large deformations of slender elements. Numerical iterative solutions are already available to solve real-time simulations. However, an assembled solution, which meets both geometric conditions and static equilibrium, is needed to start the process. A comprehensive Kinematic Analysis in the classical sense is not fully established yet. The aim of the paper is to propose a procedure that solves the full inverse and forward kinematic problems for planar three degrees of freedom systems, hence obtaining the multiple solutions arising from the closed-loop structure and the multiplicity of the deformation mode of slender links. From those solutions, finding of the different aspects that comprise the workspace is possible, as well as determining singularities and instability loci.