Synthesis method for the spherical 4R mechanism with minimum center of mass acceleration

Abstract

In the mechanisms area, minimization of the magnitude of the acceleration of the center of mass (ACoM) implies shaking force balancing. This article shows an efficient optimum synthesis method for minimum acceleration of the center of mass of a spherical 4R mechanism by using dual functions, as well as, the counterweights balancing method. Once the dual function for ACoM has been formulated, one can minimize the shaking forces from a kinematic point of view. We present the synthesis of a spherical 4R mechanism for the case of a path generation task. The synthesis process involves the optimization of two objective functions, this multiobjective problem is solved by using the weighted sum method implemented in the evolutionary algorithm known as Differential Evolution. Our results shows that the magnitude of the ACoM can be reduced about 20 times. Which for the presented synthesis, is traduced in a reduction of about 89% for the shacking forces.

Kinematics of the 3(RPSP)-S Fully Spherical Parallel Manipulator by Means of Screw Theory

“…To this aim, let us consider that the orientation of the moving platform is defined by the angles roll (γ = 3 • ), pitch (β = 2 • ) and yaw (α = 4 • ). Then, according to Equation (12), the generalized coordinates meeting this pose result in q 1 = 0.967524 m, q 2 = 1.06524 m and q 3 = 0.974468 m.…”

“…In robotics, usually this class of motion may be achieved using serial or parallel manipulators. However, the spherical motion can be performed also with a four bar spatially-closed kinematic chain with concentric revolute joints (4R) [8][9][10][11][12], which is the simplest version of a parallel manipulator.…”

Computer-aided synthesis of spherical and planar 4R linkages for four specified orientations

“…Although this method can increase the number of solutions, most of the increased linkage solutions still have motion defects, so it does not fundamentally eliminate the blindness of linkage synthesis process. Considering that modern computers can obtain massive solutions quickly and discriminate the defective linkage solutions in turn later (Myszka et al, 2009;Tipparthi and Larochelle, 2011;Bai, 2017), the method of type map (Han and Cao, 2019) is gradually applied in some linkage synthesis software, such as Synthetic (Su and McCarthy, 2005), Lincages (Erdman and Loftness, 2005), Sphinx (the latest version is SphinxPC) (Ruth and McCarthy, 1999;McCarthy, 2013) and the software developed by Han et al (2013). Among them, specially, Sphinx is the first software to solve the spherical G. Wang et al: Computer-aided synthesis of spherical and planar 4R linkages problems.…”

“…At the same time, the defective linkage solutions can be hidden. The blindness of linkage synthesis can be reduced by using the type map based on these synthesis software, but there are still some shortcomings: firstly, the biggest problem is that it is not flexible enough and must be designed the linkage according to the process set by the software; secondly, few software besides Sphinx have the synthesis ability of spherical linkage; finally, the type map method can only express the solutions distribution with different linkage type in the solution domain, however, in practical synthesis problems, the transmission performance and installation position of linkage solutions are more important than linkage types (Mendoza-Trejo et al, 2015). In order to make up for the shortcomings of the graphing method and computer-aided synthesis method mentioned above, a series of flexible functions for the synthesis, analysis and plotting of linkages are constructed under Matlab.…”