Evaluation Method and Performance Indices for the Motion/Force Constrainability of Overconstrained Parallel Manipulators Without Actuation Redundancy

Abstract Overconstrained parallel manipulators (PMs) without actuation redundancy have been widely used in various applications, such as the parallel module of the Exechon robot for workpiece machining. However, existing methods are inadequate for describing the motion/force constraint performance of nonredundant and overconstrained PMs (NOPMs) because they do not reasonably consider the influence of the overconstrained structure. This performance is crucial for evaluating the capability to resist external loads, which is of great significance for applications requiring high stiffness and precision. To address this issue, this paper proposes a new evaluation method for the motion/force constrainability of NOPMs. First, based on the four wrench and twist systems of limbs, the output constraint performances of all the single-degree-of-freedom (DOF) mechanisms under different cases can be obtained. These single-DOF mechanisms are constructed by selectively “losing” some constraint wrench screws and “locking” all the transmission wrench screws of the original overconstrained PM, which is the key step in the establishment of this method and achieved by using the ergodic method. Then, the output and input constraint performance indices in a certain configuration can be calculated, followed by the definition of a local constraint index to evaluate the motion/force constrainability of the NOPM. Notably, all the proposed indices are characterized by coordinate independence. Finally, two PMs and their corresponding overconstrained structures are simulated to demonstrate the correctness of the proposed evaluation method. The evaluation strategy can also be used for the optimal design of the NOPMs in the future.