Kinematic structure and workspace analysis of a parallel kinematic machine based on lambda mechanism with actuated translation joints

This paper presents modeling and analysis of a virtual machine prototype based on Lambda parallel kinematic mechanism with actuated translation joints. Kinematic modeling includes solving inverse kinematic and workspace analysis of the machine. Verification of inverse kinematic equations has been done analytically using MatLab software and a CAD/CAM system, and the workspace analysis is also done analytically using the polar coordinates

Workspace and Kinematic Structure Analysis of a 6-DOF Lambda Parallel Kinematic Machine

This paper presents workspace and kinematic analysis of a parallel kinematic machine based on the Lambda mechanism. The considered parallel kinematic machine has six degrees of freedom (DOF), achievable with six actuated translation joints. The kinematic analysis includes the definition of every active part of the machine, as well as the definition of every active or passive joint used to connect machine parts. The mathematical model of the machine is created for the better understanding of the machine's operation. The proposed mathematical model of the machine includes inverse kinematic equations, whose solving presents the first step in workspace analysis. In this case, the offered parallel kinematic machine has six active-joint variables, and every active-joint variable is the result of one inverse kinematic equation. Verification of the inverse kinematic equations has been done analytically, using MatLab software and a CAD/CAM system. Workspace analysis, as one of the most important parameters of the parallel kinematic machine, presents the main topic of this paper. In this case two approaches to the workspace analysis are given. The first considered analysis is used to determine the achievable workspace of the machine, and the second analysis is used to determine the total orientation workspace of the machine. Polar coordinates are used to simplify the process of the workspace analysis

Kinematic Calibration of Parallel Kinematic Machines on the Example of the Hexapod of Simple Design

The aim of using parallel kinematic motion systems as an alternative of conventional machine tools for precision machining has raised the demands made on the accuracy of identification of the geometric parameters that are necessary for the kinematic transformation of the motion variables. The accuracy of a parallel manipulator is not only dependent upon an accurate control of its actuators but also upon a good knowledge of its geometrical characteristics. As the platform's controller determines the length of the actuators according to the nominal model, the resulted pose of the platform is inaccurate. One way to enhance platform accuracy is by kinematic calibration, a process by which the actual kinematic parameters are identified and then implemented to modify the kinematic model used by the controller. The first and most general valuation criterion for the actual calibration approaches is the relative improvement of the motion accuracy, eclipsing the other aspects to pay for it. The calibration outlay has been underestimated or even neglected for a long time. The scientific value of the calibration procedure is not only in direct proportion to the achieved accuracy, but also to the calibration effort. These demands become particularly stringent in case of the calibration of hexapods of the so-called simple design. The objectives of the here proposed new calibration procedure are based on the deficits mentioned above under the special requirements due to the circumstances of the simple design-concept. The main goals of the procedure can be summarized in obtaining the basics for an automated kinematic calibration procedure which works efficiently, quickly, effectively and possibly low-cost, all-in-one economically applied to the parallel kinematic machines. The problem will be approached systematically and taking step by step the necessary conclu-sions and measurements through: Systematical analysis of the workspace to determine the optimal measuring procedure, measurements with automated data acquisition and evaluation, simulated measurements based on the kinematic model of the structure and identifying the kinematic parameters using efficient optimization algorithms. The presented calibration has been successfully implemented and tested on the hexapod of simple design `Felix' available at the IWM, TU Dresden. The obtained results encourage the application of the procedure to other hexapod structures