机构速度和加速度分析统一模型的研究

The Unified Models of Velocity and Acceleration of Mechanisms

研究了适应于任意机构的通用速度和加速度的分析模型 ,研究中采用了四个有特色的技术 :(1)基于齐次变换矩阵位移方程推导统一模型 ;(2 )在速度和加速度统一模型中使用了齐次矩阵的全部位置和姿态信息 ,这样既避免了有效方程的挑选 ,又简化了模型构造过程 ;(3)采用向量标记推导模型 ,简化了模型结构 ,同时描述了模型的构成 ;(4 )通过引入变量存在系数 ,使各个环路或构件路径的速度和加速度模型的结构形式完全一致和统一。这样 ,本文得到了统一的速度和加速度模型 ,这些模型适应于任意连杆机构 ;结构精练、标准 ;可以被自动构造 ,且构造效率高。本文为通用机构分析软件开发打下了基础。

The article develops the study of the unified models which can be used for calculating velocity and acceleration analysis in any type of mechanisms. There are four characteristic technologies adopted in the study: (1) The position-functions in the style of homogeneous transformation matrix have been used to deduce the models. (2) All the information of the orientation and location of the homogeneous transformation matrix have been used in the models, so the difficulty of selecting the all independent functions is avoided and the constructing procedure is simplified. (3) The vector mark is adopted to simplify the structure and to depict the composition of the models. (4) A special symbol which describing whether a variable is existent in a loop or in a rout has been introduced to unify the form of the model in different loop or different route. In this way, the general models of the velocity and the acceleration, have been obtained. The models have many advantages: 1) they are suitable for any mechanisms. 2) the structures of the models are concise and standard, and 3) they can be constructed automatically and efficiently. The models deduced in the article supply the base for developing a general software of kinematics analysis of mechanism.