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Modern motion control adopts acceleration/deceleration before interpolation (ADBI) motion planning to eliminate path command errors. However, the individual velocity profiles might not be continuous at the junction of the blocks. Acceleration/deceleration after interpolation (ADAI) method may provide an alternative for solving the discontinuous problems, but it causes path command errors. In this paper, an integrated acceleration/deceleration interpolation (IAD) scheme which integrates the ADBI and ADAI modules is proposed. The ADBI provides a look-ahead function which plans the feedrate profiles based on chord errors, command errors, curvatures, and acceleration limits. Within the look-ahead function, the command error equation is utilized to determine the feedrate at the junction of adjacent blocks. Then the ADBI performs non-uniform rational B-spline (NURBS) interpolation using the planned feedrate profile and outputs the position points to the ADAI module. The ADAI module processes the points by a digital convolution technique such that the continuity of the block junction velocity is ensured. Finally, the IAD is applied to the multi-block NURBS interpolation to validate its effectiveness. Simulations and experiments are conducted to demonstrate the IAD scheme. It is shown that the IAD scheme can reduce the acceleration significantly at the junctions of the blocks under the given tolerance of the command error. Furthermore, the proposed algorithm can improve tracking and contour accuracies as compared to the hybrid multi-blocks look-ahead approach. [ABSTRACT FROM AUTHOR]

Abstract: Methodologies for planning motion trajectory of parametric interpolation such as non-uniform rational B-spline (NURBS) curves have been proposed in the past. However, most of the algorithms were developed based on the constraints of feedrate, acceleration/deceleration (acc/dec), jerk, and chord errors. The errors caused by servo dynamics were rarely included in the design process. This paper proposes an integrated look-ahead dynamics-based (ILD) algorithm which considers geometric and servo errors simultaneously. The ILD consists of three different modules: a sharp corner detection module, a jerk-limited module, and a dynamics module. The sharp corner detection module identifies sharp corners of a curve and then divides the curve into small segments. The jerk-limited module plans the feedrate profile of each segment according to the constraints of feedrate, acc/dec, jerk, and chord errors. To ensure that the contour errors are bounded within the specified value, the dynamics module further modifies the feedrate profile based on the derived contour error equation. Simulations and experiments are performed to validate the ILD algorithm. It is shown that the ILD approach improves tracking and contour accuracies significantly compared to adaptive-feedrate and curvature-feedrate algorithms. [Copyright &y& Elsevier]

This paper presents the direct kinematics solutions for a novel 3-PRS parallel mechanism. The geometric method is applied to formulate three coupled trigonometric equations. One algorithm for solving the three coupled equations is to use the Bezout’s elimination method which leads to a total of 64 solutions. By categorizing the 64 solutions into six groups and further examining the corresponding configuration for each group, the preferred solution to the direct kinematics problem can be obtained. The other approach for solving the coupled equations is to apply the optimization techniques with side and behavior constraints set by analyzing undesired configurations. This approach can obtain the preferred solution without checking all the possible solutions. Moreover, it can perform more efficiently than the elimination method. [Copyright &y& Elsevier]