On Constraints and Parasitic Motions of a Tripod Parallel Continuum Manipulator

A parallel continuum manipulator (PCM) is a mechanism of closed-loop morphology with flexible elements such that their deformation contributes to its mobility. Flexible hexapods are six-degrees-of-freedom (DoF) fully parallel continuum mechanisms already presented in the literature. Devices of reduced mobility, i.e., lower mobility than six DoF, have not been studied so far. An essential characteristic of lower mobility mechanisms is that reduced mobility is due to kinematic constraints generated by mechanical arrangements and passive joints. In rigid-link parallel manipulators, those constraints are expressed as a set of equations relating to the parameters representing the end effector's pose. As a consequence, independent output pose variables are controllable with the position equations, while dependent output variables undergo parasitic motions. In this paper, the performance of a tripod-type parallel continuum manipulator, 3PF_S, is compared with the operation of its rigid counterpart 3P_RS. We will show that in PCMs there are no such geometric constraints expressible with algebraic equations, but it is difficult to perform some types of motion in the end effector with the input torques. Another goal of this paper is to evaluate such limitation of motion in a tripod-like PCM and compare it with the constraints of the rigid 3P_RS. Finally, the paper shows that there are strong similarities in the reduced mobility of both mechanisms.