Study Of Lower-mobility Over-constrained Parallel Mechanisms

With the application of modern mathematical theory in mechanics,the development of mechanisms from plane to space,from single degree of freedom to multi-freedom,from series mechanisms to parallel and hybrid mechanisms,many new mechanisms have emerged.How-ever,there are also a special kind of mechanisms-over-constrained parallel mechanisms.Because of the over constraint in mechanisms,it is difficult to calculate the degree of freedom of the mechanisms accurately.In addition,there are static indeterminate problems in the force analysis of over-constrained mechanisms.Firstly,the definitions of over constraint and over-constrained mechanisms are defined.Then,based on screw theory,the fundamental reasons for emerging over constraints in mechanisms and how to identify over constraints in mechanisms are analyzed systematically.Finally,over-constrained mechanisms are classified according to the types of over constraints and orders of mechanisms.The unique characteristics of over-constrained parallel mechanisms are analyzed by using screw theory.It is concluded that over constraint in mechanisms will be emerged in closed kinematic chain when some special configuration of kinematic pairs or structural parameters of mechanisms must satisfy some special geometric conditions.Therefore,a method of adding deformation compatibility equation of over-constrained mechanisms based on geometric condition invariance is proposed,and the force analysis of 3-RCR parallel over-constrained mechanism with three times static indeterminate is carried out.Based on 3-PRRR parallel mechanism,a 5-DOF decoupled over-constrained hybrid mechanism is proposed.Firstly,the degree of freedom and over constraints of the mechanism are analyzed by screw theory;Secondly,the position equation of the mechanism is established by analytic vector method,and kinematics and Workspace of the mechanism are carried out based on the inverse position equation;Thirdly,the dynamic model of the mechanism is established by combining Newton-Euler method with virtual work principle,and then the active force and the restraint reaction force of each joint are also solved according to the dynamic model of the mechanism have established.Finally,A display adjustment bracket system for face recognition is proposed based on the 5-DOF hybrid mechanism,which embodies the unique advantages and application value of the mechanism.