Spherical Bodies Adjoint Approach And Kinematic Geometry

In this dissertation, the infinitesimal kinematics of spherical mechanisms is analyzed and the distribution of some special characteristic points or lines on the moving body are located by means of the adjoint approach in differential geometry language. Based on the adjoint approach, the model of kinematics of spherical mechanisms is proposed at first. Then, the points with special kinematics characteristic are located, include moving pole points, fixed pole points, acceleration vanishing point, points of vanishing normal acceleration, the direction changing points, etc. The shape of the locus of both moving pole axis and fixed pole axis are discussed. After that, some points on the moving shell, whose path has special curving characteristic, such as inflection points, Ball抯 points, circle-points, are discussed and their distributions are readily located. The geometric meaning of the spherical counterpart of the Euler-Savary equation is pointed out also. Therefore, the distribution law of coupler curves with various shapes is revealed by means of the above mentioned results. At last, the three kinds of the mechanisms ?planar, spherical and spatial mechanisms are compared to show the adjoint approach composed a pedigree and to point out all of the three can be analyzed by this method.