质点与刚体相对运动的几何直解法

Direct Solution Method for Kinematical Problems of Particles and Rigid Bodies

土木建筑、车辆机械等工程领域的许多技术问题,在一定条件下可以用运动学的原理和方法加以解决;运动学传统的解题方法是“先拆解,后合成”,但这样的解题方法有时也存在一定的不方便或不足之处,譬如较为抽象、不够直观、适用面窄等。在前人研究的基础上,提出一种以标量计算为主的简化求解思路,不妨称之为“直解法”,即首先直观地表达运动学问题中的几何图形,列出几何关系方程后,按要求令等式两侧对时间求一阶或二阶导数,最终代入已知的初始或边界条件后求解方程组。直解法具有直观性强、适用面广、能够处理高阶运动学问题、便于计算机程序大规模高速度辅助运算等优点。

Many technical problems in the engineering fields such as civil engineering and vehicle machinery,can be solved by the principles and methods of kinematics under certain conditions.Traditional problem-solving method of kinematics is“disassemble first,then synthesize”;however,there are also some inconveniences or deficiencies in such method occasionally–it is abstract,not intuitive,and narrowly applicable.On the basis of previous research,this paper proposes a simplified solution idea based on scalar calculation,which may be called“direct solution method”,that is,firstly express the geometric figures in the kinematics problem intuitively,and then list the geometric relationship equations.According to the requirements,make the first or second derivative with respect to time on both sides of the equation,and finally solve the equation system after substituting the known initial or boundary conditions.The direct solution method has the advantages of strong intuition,wide applicability,ability to deal with high-order kinematic problems,and convenience for large-scale and high-speed auxiliary operations of computer programs.