Differential Kinematics for Calibration, System Investigation, and Force Based Forward Kinematics of Cable-Driven Parall
In this paper the differential kinematics for cable-driven robots is derived and the use for calibration, system investigation and a force based forward kinematics is shown. The Jacobians for each part of the kinematic chain are derived with respect to th
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Abstract In this paper the differential kinematics for cable-driven robots is derived and the use for calibration, system investigation and a force based forward kinematics is shown. The Jacobians for each part of the kinematic chain are derived with respect to the platform pose and the most important system parameters. Beside the consideration of geometrical quantities, the differential relations between non-geometrical quantities such as cable stiffness and cable forces are determined. The decomposition in the most fundamental Jacobians allows to analyse and compute more complex relations by reassembling the Jacobians as needed. This approach allows more insight in the system behavior and enables the reuse of the individual modules. The purpose of this paper is to provide the framework and the key equations and to show the use for calibration, force based forward kinematics and system analysis as well as for control purposes. Keywords Cable-driven parallel robot · Wire robot · Differential kinematics · Jacobian · System stiffness · Auto calibration · Least squares · Forward kinematics · Cable forces · Elasto-kinematic model
P. Miermeister (B) · W. Kraus · A. Pott Fraunhofer Institute for Manufacturing Engineering and Automation IPA, Nobelstrasse 12, 70569 Stuttgart, Germany e-mail: [email protected] W. Kraus e-mail: [email protected] A. Pott e-mail: [email protected] T. Bruckmann and A. Pott (eds.), Cable-Driven Parallel Robots, Mechanisms and Machine Science 12, DOI: 10.1007/978-3-642-31988-4_20, © Springer-Verlag Berlin Heidelberg 2013
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Fig. 1 Cable-driven parallel robot demonstrator at Fraunhofer IPA
1 Introduction Cable-driven parallel robots, here simply called cable robots, are parallel kinematic machines mainly consisting of a platform, cables and winches. The cables connect the platform to the winches which control the platform pose by changing the cable length. In recent years, cable robots got lots of attention due to their advantages over serial kinematic robots and conventional parallel kinematic robots with rigid links [1, 4]. On the one side, cable robots inherit the properties of parallel kinematic robots as for instance high stiffness, payload and very good precision. On the other side, they outperform conventional parallel kinematics with regards to flexibility, workspace and speed, because the cables allow ultra light weight constructions in nearly arbitrary large areas. The winches can be easily attached to solid structures as steel frames or walls and allow to change the robot configuration in a short time. The applications for cable robots include pick and place tasks, video recording for sport events as well as virtual reality simulators. It is also possible to invert the principle of actuation by exchanging the motors with passive positioning sensors which allows the cable robot to be used as metrology system (Fig. 1). All the tasks need an accurate robot model in order to provide good results. The correct mod
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