Elastostatic Performance Evaluation of a Full-Mobility Parallel-Kinematics Machine With Flexible Links

The subject of this article is the elastostatics of a novel three-limb, full-mobility parallel-kinematics machine (PKM) with flexible links, intended for high-frequency, small-amplitude operations. The objective is to establish the Cartesian stiffness model and performance indices capable of guiding the structural design of the machines of interest. We base our analysis on what we term an elastostatic Cartesian model: the light-weight limb rods are modeled as identical, massless, linearly elastic beams; the motor shafts and couplings are modeled likewise, with the beams replaced by identical, massless, linearly elastic torsional springs, both link flexibility and actuator flexibility thus being considered. The moving platform is assumed to be the only moving rigid body of the machine. This platform is thus regarded as a rigid body elastically mounted onto the base platform via a six-degree-of-freedom (six-DoF) Cartesian spring. Then, the PKM $6×6$ Cartesian stiffness matrix, considering the flexibility of both limb rods and motor shafts, is derived via the pertinent kinetostatic relations. Moreover, three alternative indices are defined from this model to evaluate the robot stiffness, which allows us to choose the most appropriate one for specific applications.