Studies On The Kinematic Morphology Of Pin-Bar Mechanisms

There are more and more mechanism analysis in modern structure designing. Many kinds of new type spatial structures such as tensegrity and deployable structures are classified to traditional mechanisms. At the same time, during the construction of some large-scale structures, the principle of mechanical motion are widely used. The analysis of kinematics morphology is very important in the research of mechanism. This paper takes singer-mechanism-mode pin-bar system as example, and pays attention to the movability of pin-bar system, the strategy to track the kinematic paths and bifurcation points.The paper sets a view to the energy criteria of stability, and instructed the movable characters and geometrical stability of pin-bar systems. Then the paper points out that traditional analysis of movable characters is a special kind of stability analysis. Actually, the Maxwell Code and balance matrix criteria are degenerate solutions deduced from the positive definite of second-order variation of system potential energy The paper recalls the constitutes of pin-bar equilibrium matrix particularly as well as singular-value deposition method. Also the paper tells the physical meaning of four sub-space vectors in the equilibrium matrix in detail.The paper points out it fault to judge the movability of pin-bar systems with Maxwell code or balance matrix criteria. The mean points is that these two criteria responses to second-order variation of system potential energy. The paper sets the view to the energy and analyses the movability of a special pin-bar system which contains a infinitesimal mechanical mode. The results tells the movability should be judged by the positive definite of higher-order variation of system potential energy.The paper proves that the equilibrium equation is the controller equation for the kinematics morphology of mechanisms, and the solution of kinematic paths can take advantages of the physical characters of mechanical modes. Then the paper brings forward a strategy to track the kinematic paths, and deduced the related iteration expression. After the examination of an example, the paper proves the correctness of the strategy.The paper points out that the bifurcation of kinematic path is multiresolution of the equilibrium equation. According the matrix theory, the multiresolution can be got by tracking the numbers of the none-zero singular values of the balance matrix. During the process to calculate the mathematic solution of the kinematic path, the paper finds the bifurcation pointsusing tracking the variety of minimal singular value of the balance matrix. Also the examination shows it's valid to find the bifurcation points.The author make the process to track the kinematic path and determine the bifurcation points. Two examples have been analysed by the process. Meanwhile the author works on the source of the error and points out how to lighten its influence.