A novel index to evaluate the mapping of parallel mechanisms from internal to external wrenches. (January 2021) - Wang, Chang
Highlights: A novel index is built based on the whole wrench mapping matrix. Constraint loads, driving loads, and rigid body loads are considered. The physical interpretation of the index is explained and analyzed. Abstract: A mechanism not only bears loads on the output but also endures loads from gravity, inertia, and other types of stresses from the environment on all rigid bodies (or links). These loads are collectively called external wrenches. Internal wrenches, which include the constraint loads of joints and the driving loads of actuators, resist external wrenches. Mapping from internal to external wrenches can provide an extensive evaluation of the mechanism considering all the constraint loads of the joints, the driving loads of the actuators, and all the possible loads of each rigid body. This paper proposes a novel index that can evaluate a mechanism by considering both the internal and external wrenches. First, the whole wrench mapping matrix from the internal to the external wrenches is built based on the digraph connections of the rigid bodies. Second, with the condition number of the matrix, the whole wrench index is obtained to evaluate the mapping from internal to external wrenches, and its physical interpretation is studied. Finally, two kinds of parallel mechanisms are analyzed to indicate the significance and universality of the novel index.