Kinematic path analysis of kinematically indeterminate systems

Abstract

Kinematically indeterminate systems are geometrically unstable. Considering that there is only tiny elastic deformation in the process of the mechanism motion, the method to simulate kinematic paths of kinematically indeterminate systems without considering elastic deformation is studied in this paper. Based on the equilibrium matrix theory, mechanism displacement is decomposed into combinatorial displacement of independent inextensional mechanisms and displacement resulted from the length modifications of members. The reasonable combination coefficient of inextensional mechanisms is determined by the gradient of the potential energy. An analysis algorithm is developed to simulate the kinematic paths of rigid pin-bar assemblies. The validity and accuracy of the algorithm proposed in this paper is illustrated by three typical examples.

A rule-based exclusion method for tolerance specification of revolving components

“…Let FR R be the variation requirement of a revolving feature. The variation of a feature can be decomposed into form variation FR 1 , rotation variation FR 2 and translation variation FR 3 , according to the kinematics 35 and tolerance analysis method 36 (see Figure 4). Based on the definition of the tolerances, FR 1 can be controlled by the form tolerance, FR 2 by the orientation tolerance and FR 3 by the position tolerance.…”

“…Let FRR be the variation requirement of a revolving feature. The variation of a feature can be decomposed into form variation FR1, rotation variation FR2 and translation variation FR3, according to the kinematics 35 and tolerance analysis method 36 (See in Fig. 4).…”

Modeling and Kinematic Path Selection of Retractable Kirigami Roof Structures

“…Moreover, based on the equilibrium matrix of the mechanism and the virtual work principle, Yuan et al. () proposed a new method to simulate the motion path.…”

“…Recently, Yuan et al (2012) proposed an analogous stiffness method, which is defined as the derivative of the state variable with respect to the controlling variable, to predict the singularity and kinematic bifurcation of mechanisms. Moreover, based on the equilibrium matrix of the mechanism and the virtual work principle, Yuan et al (2016) proposed a new method to simulate the motion path.…”