两维并联雕刻机工作台研究

【作者】 王超群；

【导师】 吴洪涛；

【作者基本信息】 南京航空航天大学 ， 机械电子工程， 2003， 硕士

【摘要】 本文提出了两种平面两自由度并联平台：2(?)RR型和2R(?)R型(前者的驱动副为转动副，后者的驱动副为移动副)，它们来源于有较多研究的3(?)RR型和3R(?)R型并联机构，系将其中的某个自由度加以约束而得到。本文以2(?)RR型为主进行了深入研究。他们皆可应用于小型雕刻机的工作台。众所周知，运动学正解、工作空间求解和奇异性分析是并联运动学机器的三大关键问题，本文所论及的两种平台也不例外，不过由于创造性地约束了3自由度机构的转动自由度，使所得的新型2自由度机构2(?)RR的基本关键问题得到简化，从而更具实际应用价值。 运动学分析是研究工作的基础，因此成为本文的重要部分。本文得到了两种平台的正反运动学解的解析表达式。其中2(?)RR型平台的反向运动学解有4组，正向运动学解有两组；而2R(?)R型平台的反向运动学解是唯一的，正向运动学解有两组。由此可见，2R(?)R型平台较2(?)RR型平台控制更容易。 奇异性分析是并联运动学机器的又一个关键问题。本文鉴于所得到的正向和反向运动学解的解析表达式，进一步获得了2(?)RR型并联平台的完整奇异性条件，分为三种情况，由此为下一步物理样机的研制和控制奠定了坚实的基础。为了清楚地观察奇异形位的特征，本文还得到了奇异表达式的多项式形式。在奇异分析和工作空间分析的基础上，绘制了奇异曲线和平台的工作空间边界。 为掌握所研究的2(?)RR型并联平台的动态特性、使并联机器的优点得以在雕刻机中充分发挥，本文还应用拉格朗日方法建立了机构的动力学模型，并进行了初步的动力学分析。并进一步利用OpenGL和VC++软件、ADAMS虚拟样机分析软件对平面两自由度并联雕刻机进行了造型和仿真，取得了较为满意的效果。更多还原

【Abstract】 Two types of 2-dof planar parallel platforms (2RRR and 2RPR) are addressed in this paper. They are rooted in 3-dof parallel frameworks (3RRR and 3RPR) that have been studied in many aspects and are gained by restricting its certain degree of freedom. These two platforms are lucubrated mainly on the former. They are all used in worktable of small sculptor. As most of us known,forward kinematics,workspace and singularity analysis are three pivotal problems of parallel kinematic machine. These problems are not exceptional to the two platforms discussed in this paper. But these analyses of the two platforms are simplified for restricting the revolving degree of freedom of the 3-dof frameworks in a creative way.Kinematics analysis is basis of the research work so it becomes the most important section in this paper. An analytical form of the forward and inverse kinematics is derived. The 2RRR platform has four different branches of inverse kinematics and two of forward kinematics,while the 2RPR platform has one and only inverse kinematics and two of forward kinematics. Thus it can be seen that the control of 2RPR platform is easier than the 2RRR platform.Singularity analysis is second pivotal problem of parallel kinematic machine. Based on analytical expressions of the forward and inverse kinematics,complete singularity conditions of 2RRR parallel platform are derived,which accordingly establish firm base for the development and control of physical prototype. To observe the character of singularity loci clearly,a polynomial form of the singularity loci are also derived. Based on the singularity and workspace analysis,the graphical representation of the complete singularity loci and workspace limits is illustrated with example.To grasp dynamic character of the 2RRR parallel platform and to exert the advantage of parallel machine in sculptor well,dynamics model of the platform is founded by using Lagrangian approach and dynamic analysis are made primarily. By using the VC++ and OpenGL software and the ADAMS software,the simulation and modeling of the planar 2-dof parallel sculptor are completed,and comparatively satisfactory effect is obtained.更多还原