平面梯形机构不能精确实现无侧滑转向的证明

Proof on Impossibility for Any Plane Trapezoid Linkage to Reproduce Ackermann Steering Exactly

基于“转向机构不可能精确实现无侧滑转向”的预先判断 ,多年来人们对轮式车辆各种转向机构做了大量优化设计工作。然而迄今为止没研究过该判断是否正确。转向机构中最具代表性的整体式等腰梯形机构常被简化为平面等腰梯形机构进行设计。在此情况下 ,本文通过将实际转向角方程和无侧滑方程对比 ,证明上述判断是正确的 ,即该种平面机构不能使车辆在任意转弯半径下都做精确的无侧滑转向。

For many years past, based on a prejudgement that it is impossible to exactly reproduce Ackermann steering of a wheeled vehicle by any steering linkage, a lot of work have been done on optimum designs of various steering linkages. However, the judgement still remains to be verified so far. Isosceles trapezoid linkage, a kind of most representative steering linkage, was usually designed in its simplification to a plane isosceles trapezoid linkage. In this case, by making a comparison between actual steering angle equation and Ackermann steering equation in this paper, the correctness of the judgement is proved, i.e., the plane linkages can't make vehicles exact Ackermann steering at every arbitrary turning radius. This provide a solid theoretical base for approximate and optimum design of plane isosceles trapezoid steering linkages.