A DBB-Based Kinematic Calibration Method for In-Parallel Actuated Mechanisms Using a Fourier Series

Abstract

For kinematic calibration of robots, we proposed using a low order Fourier series obtained by transforming the data for circular measurements paths. The paths were measured using a Double-Ball-Bar (DBB) system. Two nondimensional indices were proposed for evaluating the orthogonalities of the measurement paths and calibration parameters. An index was also proposed to evaluate the accuracy of the calibration with regard to measurement error. An algorithm for determining adequate measurement paths and an optimal set of a specified number of paths using these indices was also proposed. The effectivenesss of the porposed method, indices, and algorithm was investigated through simulations and experiments of kinematic calibration with an experimental in-parallel actuated worktable which we developed.

A study on tolerances design of parallel link robots based on mathematical models

“…As shown in the figure, the trajectory of the end effector has an ellipsoidal shape, and the radial positioning deviations reach about ±0.4 mm. The patterns and the ranges of the radial deviations obtained here are almost same as the results published by the other papers (Takeda et al 2004).…”

A method for kinematic calibration of a parallel robot by using one camera in hand and a spherical object

“…θ r θ r θ r θ r , y x x u 1 x u e = x u 1 x u e = x u 1 x u e = x u 1 x u e = Centroid Substituting (18) in (21) and clearing for ܽ and ߠ finally: Fig. 8 Angle ߠ .…”

“…External calibration can be done by measuring completely or partially the pose parameters of the platform. Measurements of the pose of a platform can be done with a laser and a coordinate measuring machine (CMM) [5], commercial visual systems (optical system and infrared light) [6][7][8], visual systems and microscopes [9], laser sensor [10], by adding passive legs [11] or by constraining elements [12], with a interferometer [13], with a LVDT and inclinometers in [12,14], theodolite [15], with gauges [16], with double ball bar (DBB) [17,18], by inspecting a machined part that is dedicated to the calibration process [19], accelerometers [20], or with visual systems and patterns widely studied (chess-board and similar patterns) [21][22][23]. Above examples are different strategies that obtain kinematic information of the robot, but in general, calibration methods impose virtual or real constraints on the poses of the end effector (or mobile elements).…”

Calibration of Parallel Manipulators and their Application to Machine Tools. A State of the Art Survey

“…Error parameters for the three planes method were obtained in order to implement error measurement and error compensation. Takeda et al (2004) proposed the use of a low order Fourier series obtained by transforming the data for circular measurement paths by using a 6 dof in-parallel actuated worktable. The errors of the realized paths were measured using a DBB system.…”