【作者】 王科；

【导师】 赵亮；

【作者基本信息】 浙江大学 ， 机械设计及理论， 2010， 硕士

【摘要】 SCARA运动学的研究中,以旋量,李群李代数为基础的POE指数积法求解运动学正解,逆解以及速度雅可比。逆解中采用代数的方法求解封闭解,得出了逆解方程。以POE指数积方法求解中,因为坐标系的建立,以及相应坐标系之间的位置关系都以旋量描述,使得整个求解过程较传统的求解方法更为简单。以雅可比矩阵为基础,对SCARA的奇异性进行分析。根据SCARA机器人独特的机构形式进行了必要的简化,找出其完全展开的边界为奇异。SCARA的奇异性分析中,发现SCARA的奇异性分析更加类似于平面二连杆的求解。将旋量理论引入误差分析,建立机器人运动学的误差旋量模型,分析误差源在执行端所造成的误差空间的特点。引入等效半径的误差敏度评价体系,分析不同量纲误差对执行端误差空间的影响。通过对单独误差及总的误差空间的评价与分析,给不同精度要求的工业机器人设计提供有效的理论支持。轨迹规划中,分析了关节空间的多项式插值的优缺点。最终以余弦函数对惯性空间的规划轨迹进行插值离散。经插值后关节空间的速度和加速度的线图轨迹平滑。应用旋量理论建立SCARA机器人的运动学模型,并以此为基础建立动力学模型。此方法融合了拉格朗日,牛顿—欧拉法以及旋量的特点,易于求解。简要讨论动力学与机器人控制、设计的关系。更多还原

【Abstract】 In the study of SCARA’s kinematics, POE is used to obtain positive, inverse and jacobian solution, based of screw, Lie groups and Lie algebra. Algebraic method is used to form solving equation and obtain closed-form solution for inverse kinematics. Using POE to solve the problem is much simpler than traditional methods, as coordinate is established and the relation between them is described by screw theory.Singularity of SCARA based on jacobian matrix is analyzed and the result indicates that singularity analysis is similar to the solution of planar two-link. It simplifies the problem for SCARA robot’s unique mechanism and finds that the position at the boundary of fully expanded SCARA is singular.This paper introduces the screw theory to the error analysis, builds a screw-error model based on robot kinematics, and analyzes the characterization of error space which is induced by error sources in operative mechanism. The equivalent radius error sensitivity evaluation system is introduced to analyze the effects of error space when different dimensional errors are put on operative mechanism. It provides effective theoretical support for industrial robot design which requires different accuracy through evaluation and analysis of single error and the total error space.This paper analyzes the strengths and weaknesses of Multinomial Interpolation for joint space in Trajectory planning. Eventually it adopts cosine function for discrete interpolation in the inertial space trajectory planning. The trajectories stand for the velocity and acceleration of joint space after interpolation are smooth.The kinematics model and dynamics model are built for SCARA robot using screw theory. This method combines the features of Lagrange method, Newton - Euler method and screw theory, and is easy to solve. The relationship between robot design, control and the dynamics is discussed briefly.更多还原