Optimal Design of Parallel Kinematics Machines with 2 Degrees of Freedom

Abstract

The mechanical structure of today’s machine tools is based on serial kinematics in the overwhelming majority of cases. Parallel kinematics with closed kinematics chains offer many potential benefits for machine tools but they also cause many drawbacks in the design process and higher efforts for numerical control and calibration. The Parallel Kinematics Machine (PKM) is a new type of machine tool which was firstly showed at the 1994 International Manufacturing Technology in Chicago by two American machine tool companies, Giddings & Lewis and Ingersoll. Parallel Kinematics Machines seem capable of answering the increase needs of industry in terms of automation. The nature of their architecture tends to reduce absolute positioning and orienting errors (Stan et al., 2006). Their closed kinematics structure allows them obtaining high structural stiffness and performing high-speed motions. The inertia of its mobile parts is reduced, since the actuators of a parallel robot are often fixed to its base and the end-effector can perform movements with higher accelerations. One drawback with respect to open-chain manipulators, though, is a typically reduced workspace and a poor ratio of working envelope to robot size. In theory, parallel kinematics offer for example higher stiffness and at the same time higher acceleration performance than serial structures. In reality, these and other properties are highly dependent on the chosen structure, the chosen configuration for a structure and the position of the tool centre point (TCP) within the workspace. There is a strong and complex link between the type of robot’s geometrical parameters and its performance. It’s very difficult to choose the geometrical parameters intuitively in such a way as to optimize the performance. The configuration of parallel kinematics is more complex due to the high sensitivity to variations of design parameters. For this reason the design process is of key importance to the overall performance of a Parallel Kinematics Machines. For the optimization of Parallel Kinematics Machines an application-oriented approach is necessary. In this chapter an approach is presented that includes the definition of specific objective functions as well as an optimization algorithm. The presented algorithm provides the basis for an overall multiobjective optimization of several kinematics structures. An important objective of this chapter is also to propose an optimization method for planar Parallel Kinematics Machines that combines performance evaluation criteria related to the following robot characteristics: workspace, design space and transmission quality index.