Abstract: Link bar coordinate systems are established based on axis direction of joint axis; coordinate system transformation matrix is derived according to Denavit-Hartenberg（D-H） notation. Forward kinematics model is set up in the light of coordinate system transformation matrix. Inverse kinematics model is set up based on forward kinematics model at last. The forward kinematics model is a nonlinear constraint optimization problem. For the purpose of sloving inverse kinematics model, new differential evolution algorithm is proposed based on the idea of multi-population and multi-mutation strategy. Multi-population strategy improves the ability of information sharing by individuals, and multi-mutation method promotes the diversity of individuals, and the numerical results indicate that the new algorithm can solve inverse kinematics model efficiently.

Key words: robot arm, joint, degree of freedom

摘要： 根据机械臂关节轴线方向建立了连杆坐标系，采用Denavit-Hartenberg（D-H）法得到连杆坐标系变换矩阵，通过坐标系变换矩阵得到机械臂正运动学模型，由正运动模型得到机械臂逆运动学模型。该模型是一个非线性约束优化问题。为了求解模型，基于多种群和多变异策略，提出了多变异策略的多种群差分演化算法。多种群策略可以提升个体共享群体信息的能力，多变异模式策略可以提升个体间的差异性，数值试验表明新算法可以有效求解机械臂逆运动学模型。

关键词: 机械臂, 关节, 自由度