可重构球面并联机构的构型设计与工作空间求解方法

发布时间：2018-10-29 23:09

【摘要】：可重构并联机构因其具有良好的适应性以及结构和功能的可变特性成为并联机构领域的研究热点之一。球面并联机构作为并联机构的一种特殊类型,不仅具备了并联机构本身承载能力大、结构刚度大、结构对称以及运动惯性小等特点,而且末端始终在以所有转动副轴线的汇交点为球心的球面上运动,工作空间为球面的一部分,具有空间三维转动的运动特点,可作为卫星天线的方位跟踪系统,也可作为仿生机构的腕关节、肩关节、腰关节、球面雕刻机以及各类航空器的地面自动跟踪设备的结构方案。本文以3-RPR和3-RRP球面并联机构为原型机构,3-RPRP球面并联机构为研究对象,研究可重构球面并联机构构型的可重构方法、运动学性能及其工作空间求解方法。全文的主要工作如下:首先,集成3-RPR和3-RRP两种原型球面并联机构,使得每条支链上均有四个运动副。通过部分运动副的自锁完成不同构型之间的转换。根据自锁的运动副数目及其位置进行排列组合,集成后的球面并联机构的运动支链在不进行拆除替换的情况下可重构出10种不同自由度以及不同构型的运动支链,其中包括两种原型机构的运动支链,实现了构型之间的无拆解重构。以驱动的安装位置作为可重构3-RPRP球面并联机构的设计依据,确定RPRP型支链中驱动副以及自锁运动副的位置。根据支链的运动副类型和组合顺序,对可重构3-RPRP球面并联机构的结构进行了设计。其次,基于螺旋理论建立了可重构3-RPRP球面并联机构的各个构态的运动螺旋系以及反螺旋系,求出了可重构3-RPRP球面并联机构在不同构态下的公共约束数和运动特性,对机构的自由度进行了求解。以机构的几何关系为约束条件,用旋转矩阵建立了机构的运动学位置封闭正解数学模型。然后,提出了一种用于求解可重构球面并联机构可达工作空间的三维动态求解法。运用该求解方法获得了3-RPRP球面并联机构的可达工作空间。基于机构的位置正解,运用Matlab软件编程求解也获得了3-RPRP球面并联机构的可达工作空间。两种求解方法的结果进行了对比,其可达工作空间面积的误差率为0.09%,验证了提出的三维动态求解法的正确性。对对称型3-RPR球面并联机构的尺度进行了综合。最后,用SolidWorks软件建立了可重构3-RPRP球面并联机构的虚拟样机,根据目标轨迹进行了运动学和动力学的模拟仿真,分析了机构输入与输出之间的耦合关系。本文设计的可重构球面并联机构实现了构型之间的快速重构,扩大了机构的应用范围以及增强了机构对环境的适应能力。提出的工作空间的三维动态求解法不仅准确率高而且可应用于其他多种类型的并联机构。
[Abstract]:Reconfigurable parallel mechanism has become one of the research hotspots in the field of parallel mechanism because of its good adaptability and variable characteristics of structure and function. As a special type of parallel mechanism, spherical parallel mechanism not only has the characteristics of large bearing capacity, large stiffness, symmetrical structure and small kinematic inertia of parallel mechanism. Moreover, the end always moves on the spherical surface with the intersection point of all axis of rotating pair as the center of the sphere, and the workspace is a part of the sphere, which has the characteristic of three-dimensional space rotation and can be used as the azimuth tracking system of the satellite antenna. It can also be used as the structural scheme of wrist, shoulder, waist joint, spherical engraving machine and ground automatic tracking equipment of all kinds of aircraft. In this paper, taking 3-RPR and 3-RRP spherical parallel mechanism as prototype mechanism and 3-RPRP spherical parallel mechanism as research object, the reconfigurable method, kinematics performance and workspace solution of reconfigurable spherical parallel mechanism are studied. The main work of this paper is as follows: firstly, the two prototype spherical parallel mechanisms, 3-RPR and 3-RRP, are integrated so that there are four kinematic pairs on each branch chain. The transformation of different configurations is accomplished by self-locking of partial kinematic pairs. According to the number and position of self-locking kinematic pairs, the kinematic branching chains of the integrated spherical parallel mechanism can be reconstructed with 10 different degrees of freedom and different configurations without removing and replacing them. It includes two kinds of kinematic branching chain of prototype mechanism, which realizes no disassembly and reconstruction between configurations. The position of the driving pair and the self-locking kinematic pair in the RPRP type branching chain are determined by using the driving position as the basis for the design of the reconfigurable 3-RPRP spherical parallel mechanism. The structure of reconfigurable 3-RPRP spherical parallel mechanism is designed according to the type and combination order of the kinematic pair of the branch chain. Secondly, based on the helical theory, the kinematic helical system and the inverse helical system of the reconfigurable 3-RPRP spherical parallel mechanism are established, and the common constraint numbers and kinematic characteristics of the reconfigurable 3-RPRP spherical parallel mechanism under different configurations are obtained. The degree of freedom of the mechanism is solved. Taking the geometric relation of the mechanism as the constraint condition, the mathematical model of the kinematic position closed forward solution of the mechanism is established by using the rotation matrix. Then, a three dimensional dynamic solution method is proposed to solve the reachable workspace of reconfigurable spherical parallel mechanism. The reachable workspace of 3-RPRP spherical parallel mechanism is obtained by using this method. Based on the forward position solution of the mechanism, the reachable workspace of the 3-RPRP spherical parallel mechanism is also obtained by using Matlab software. The results of the two methods are compared, and the error rate of the reachable workspace area is 0.09, which verifies the correctness of the proposed three-dimensional dynamic solution method. The scale of symmetric 3-RPR spherical parallel mechanism is synthesized. Finally, the virtual prototype of the reconfigurable 3-RPRP spherical parallel mechanism is established by using SolidWorks software. The kinematics and dynamics simulation is carried out according to the target trajectory, and the coupling relationship between the input and output of the mechanism is analyzed. The reconfigurable spherical parallel mechanism designed in this paper realizes the rapid reconstruction between configurations, expands the application scope of the mechanism and enhances the adaptability of the mechanism to the environment. The proposed method not only has high accuracy but also can be applied to other kinds of parallel mechanisms.
【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

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