3-PPR球面并联机构运动学性能研究与应用

发布时间：2018-04-05 23:30

本文选题：球面并联机构　切入点：运动学　出处：《中北大学》2017年硕士论文

【摘要】：三自由度球面并联机构是少自由度并联机构的重要分支。动平台上的参考点在球面上运动。由于其特殊的运动轨迹,可以应用到具有球面要求的工作任务中,如:高精密的球面机械加工、航天航空的定位和测绘系统、仿生关节的结合处等。本文选择3-PPR球面并联机构为研究对象,分别从理论角度和数值验证角度研究该机构运动学特性,为3-PPR球面并联机构的产品化提供理论依据。首先,利用3-PPR球面并联机构的结构特点建立了矢量闭环方程,在静坐标系中,对该球面并联机构中运动副的位置坐标进行了计算,给出了该机构中各运动副的位置矢量,写出3条支链的运动螺旋系,计算了并联机构的自由度,且与运动螺旋系的反螺旋系进行对比分析,验证计算结果的正确性。其次,在该机构每条支链的运动螺旋系的基础上,利用螺旋理论推出反螺旋系建立约束子矩阵和运动子矩阵,再利用矩阵理论知识,对约束子矩阵和运动子矩阵组成的完整雅可比矩阵的秩进行考察计算,分析发生约束奇异和运动奇异的条件,讨论发现该机构不存在奇异位形。再次,对3-PPR球面并联机构中影响工作空间的因素进行分析,并给出影响因素的范围。结合该机构的运动正解方程,利用蒙特卡洛法搜索法,在Matlab中进行计算,求解出该球面并联机构的可达工作空间,并与该机构的奇异性进行相互验证,证明求解结果的正确性。然后,讨论了少自由度并联机构影响系数的直接法。利用各支链的运动螺旋系,给出3-PPR球面并联机构的一阶影响系数矩阵和二阶影响系数矩阵,并且利用数值法和仿真法对该并联机构的一阶影响系数矩阵和二阶影响系数矩阵进行实例验证,对比分析各方法的结果,验证影响系数矩阵的正确性。对3-PPR球面并联机构建立模型进行仿真,通过改变驱动函数的设置,并对比分析不同模式下,恒速驱动和正弦驱动对3-PPR球面并联机构运动学的影响。最后,基于脚踝运动特性的研究和脚踝康复机理对机构的要求,对3-PPR球面并联机构进行重新设计,规划出脚踝处的运动轨迹,选择适合的驱动模式,并给出示例进行仿真验证,并对比脚踝运动特性和脚踝康复机理对机构的要求,证明3-PPR球面并联机构应用在脚踝康复机器人中的可行性。
[Abstract]:Three degree of freedom spherical parallel mechanism is an important branch of low degree of freedom parallel mechanism.The reference points on the moving platform move on the sphere.Because of its special motion trajectory, it can be applied to work tasks with spherical requirements, such as: high precision spherical machining, aerospace positioning and mapping system, biomimetic joint joint, etc.In this paper, the kinematics of 3-PPR spherical parallel mechanism is studied from the point of view of theory and numerical verification, which provides a theoretical basis for the production of 3-PPR spherical parallel mechanism.Firstly, the vector closed loop equation is established by using the structural characteristics of the 3-PPR spherical parallel mechanism. In the static coordinate system, the position coordinates of the kinematic pairs in the spherical parallel mechanism are calculated, and the position vectors of the kinematic pairs in the mechanism are given.The degree of freedom of the parallel mechanism is calculated and compared with the inverse helical system of the kinematic helical system, and the correctness of the calculation results is verified by writing out the kinematic helical system of the three branched chains and calculating the degree of freedom of the parallel mechanism.Secondly, on the basis of the kinematic helical system of each branch chain of the mechanism, the inverse spiral system is derived by using the helical theory to establish the constraint submatrix and the kinematic submatrix, and then the knowledge of matrix theory is used.The rank of the complete Jacobian matrix composed of constrained submatrix and motion submatrix is investigated and calculated. The conditions for the occurrence of constrained singularity and motion singularity are analyzed. It is found that there is no singular configuration in the mechanism.Thirdly, the factors affecting workspace in 3-PPR spherical parallel mechanism are analyzed, and the range of influencing factors is given.Combined with the forward kinematic equation of the mechanism and the Monte Carlo search method, the reachable workspace of the spherical parallel mechanism is calculated in Matlab, and the singularity of the mechanism is proved to be correct.Then, the direct method of the influence coefficient of the small degree of freedom parallel mechanism is discussed.The first order influence coefficient matrix and the second order influence coefficient matrix of 3-PPR spherical parallel mechanism are given by using the kinematic helical system of each branch chain.The first order and second order influence coefficient matrices of the parallel mechanism are verified by numerical method and simulation method. The results of each method are compared and analyzed to verify the correctness of the influence coefficient matrix.The model of 3-PPR spherical parallel mechanism is simulated and the effect of constant speed drive and sinusoidal drive on the kinematics of 3-PPR spherical parallel mechanism is analyzed by changing the setting of driving function.Finally, based on the research of ankle motion characteristics and the requirements of ankle rehabilitation mechanism, the 3-PPR spherical parallel mechanism is redesigned, the motion trajectory of the ankle is planned, the suitable driving mode is selected, and an example is given to verify the simulation.By comparing the ankle motion characteristics and the mechanism of ankle rehabilitation, the feasibility of applying 3-PPR spherical parallel mechanism to ankle rehabilitation robot is proved.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH112;TH789

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