相伴曲面方法及其在机构运动几何学研究中的应用

NEW ADJOINT APPROACH AND ITS APPLICATION IN THE KINEMATIC GEOMETRY RESEARCH OF MECHANISMS

将微分几何学中的曲线与曲线相伴方法发展到曲线与直纹面、直纹面与直纹面相伴方法，应用于机构运动几何学研究。分别以约束曲线和约束曲面为原曲线和原曲面，导出了连杆运动的瞬心线或瞬轴面及其不变量的表达式，揭示了其运动学意义，加之引入不动点、不动线和准不动线条件，完整地描述了连杆点和直线的轨迹与瞬轴面的内在联系。为机构运动几何学研究提供了新的有力工具。

A new adjoint approach is developed from differential geomatry and is applied to research the kinematic geometry of planar and spatial mechanisms. The constraint curves and the constraint ruled surface of mechanisms are taken as the origin curves and the origin ruled surfaces respetively. A point trajectory and a line trajectory are visualized as an adjoint curve and an adjoint ruled surface, whose invariants are represented by that of the origin curve and surface. The centrodes or axodes are examined as a special case of the adjoint curve or the adjoint surface, whose invariants are exposed in terms of the origin curves and origin surfaces. By taking the centrodes of the planar mechanism and the axodes of the spatial mechanism as an origin curve and an origin surface, a point trajectory and a line trajectory can be treated in the same way, which lead to display the intrinsic relations among the invariants of the point trajectory, the line trajectory, the centrodes, the axodes and the parameters of the mechanism. The kinematic geometric proparties of a mechanism are revealed in terms of their invariants.