Fast Kinematic Model of a Seven-Bar Linkage With a Single Compliant Link

This work deals on a kinematical model of a parallel mechanism for biomedical applications. The mechanism is a linkage composed by three closed loops. It is composed by seven bars (one of them is the frame) constrained each other by ideal constraints (prismatic, rotary or lock joints). The ideal joints introduce 21 degrees of constraint, while the bars produce eighteen degrees of freedom when considered rigid. Six bars are really rigid, while one of them is compliant with respect to the others and allows the mobility of the mechanism. The kinematic of this seven-bar linkage is analyzed with the aim of Hermite’s polynomials. The proposed approach is based on the knowledge of kinematical constraints at the ends of the compliant beam, in terms of position and curvature. This knowledge is based on the fact that the rest of the structure is composed by rigid bodies and ideal concentrated constraints. The compliance affects the beam only with bending effects, furthermore, in this work, we consider only a planar linkage, thus the torsion effect is not considered, and the beam is constrained in ways that compression instability is negligible. Although the beam is subjected to important deformations, it is divided in parts, such that each part is subjected to a small deformation. In this way, we propose the Hermite’s polynomials to describe the shape of the beam. We tested this fast method to describe the kinematical behavior of the system with a kinetostatic model of a mechanical device, finding that it is reliable for the proposed application.