Kinematics and Dynamics of a Self-Stressed Cartesian Cable-Driven Mechanism

Abstract

A novel hybrid cable-driven mechanism with Cartesian motion is introduced. It consists of a rigid-link Cartesian mechanism and a cable drive system with stationary actuators to provide the motion. The cable drive system is self-stressed meaning that the tension in the cables required to keep them taut is provided internally and hence does not depend on either actuation redundancy or external sources such as gravity. This keeps the number of actuators at minimum and also eliminates the static loading of actuators as well as redundant work. The kinematic analysis of the mechanism is presented. The forward and inverse kinematic solutions are found and shown to be linear and pose independent. Also the stiffness of the mechanism induced by the compliance of the cable is analyzed to find the weakest stiffness. For this purpose, a parameter called “compliance length” is defined and used. Compliance length presents the stiffness of the mechanism by the length of the cable with the same stiffness. It makes the analysis independent from the design and the properties of the cable and can be quite useful in the design process. Finally, two dynamic models are given for the mechanism depending on whether or not the cable is stretchable and the properties of each model are discussed.