Exact Path Synthesis of RCCC linkages for a Maximum of Nine Prescribed Positions

This paper addresses the path synthesis of RCCC linkages, a problem that has not given due attention in the literature. Compared with planar and spherical four-bar linkages, a RCCC linkage has many more design parameters, which leads to a complex formulation of the path-synthesis problem and, consequently, to a quite challenging system of algebraic equations. In this paper, the problem is solved with a novel formulation of path synthesis for visiting a number of prescribed positions. This is achieved by means of an alternative coordinate system, with which point coordinates are expressed with the aid of two vectors fixed to the same body. By this means, the rotation matrix used to represent the coupler-link attitude is obviated. The synthesis equations are then formulated in a simple form. The new formulation confirms that path synthesis admits exact solutions for up to nine prescribed positions, which proves a landmark claim submitted by Burmester. Examples are included to demonstrate the path-synthesis procedure with the method thus developed.

Informed Latent Space Exploration for Image-Based Path Synthesis of Linkages

This paper brings together rigid body kinematics and machine learning to create a novel approach to path synthesis of linkage mechanisms under practical constraints, such as location of pivots. We model the coupler curve and constraints as probability distributions of image pixels and employ a Convolutional Neural Network (CNN) based Variational AutoEncoder (VAE) architecture to capture and predict the features of the mechanism. Plausible solutions are found by performing informed latent space exploration so as to minimize the changes to the input coupler curve while seeking to find user-defined pivot locations. Traditionally, kinematic synthesis problems are solved using precision point approach, wherein the input path is represented as a set of points and a set of equations in terms of design parameters are formulated. Generally, this problem is solved via optimization, wherein a measure of error between the given path and the coupler curve is minimized. A limitation of this approach is that the existing formulations depend on the type of mechanism, do not admit practical constraints in a unified way, and provide a limited number of solutions. However, in the machine design pipeline, kinematic synthesis problems are concept generation problems, where designers care more about a large number of plausible and practical solutions rather than the precision of input or the solutions. The image-based approach proposed in this paper alleviates the difficulty associated with inherently uncertain inputs and constraints.

Interior Sound Quality Prediction of Pure Electric Vehicles Based on Transfer Path Synthesis

The interior sound quality (SQ) of pure electric vehicles (PEVs) has become an important consideration for users purchasing vehicles. At present, it is insufficient to take the sound pressure level as the interior acoustics design index of PEVs. Transfer path analysis (TPA) and transfer path synthesis (TPS) that take the SQ of interior noise as the improvement target remains in the preliminary exploration stage. In this paper, objective psychoacoustic parameters of SQ were taken as evaluation indexes of interior PEV noise. A virtual interior SQ synthesis model was designed on the basis of TPA and TPS, which combines experimentation and simulation. The SQ synthesis model demonstrates each noise component contribution in a PEV by new SQ separation technology. First, the interior noise transfer path and noise source of the PEV were determined in a synthesis analysis method of the interior PEV noise. Second, on the basis of the composition mechanism of interior noise and the basic principle of TPA, the excitation signal and transfer function of each interior noise path in the PEV were tested. On the basis of TPS, the interior SQ synthesis model of PEV was then established. Finally, the accuracy of the prediction model was verified in simulation and experimental comparison studies on the psychoacoustic objective parameters of SQ. The SQ objective parameter value of each transfer path was quantified by using contribution analysis. The results are expected to improve the comfort of the interior acoustic environment and enhance the competitiveness of vehicle products. They also provide an effective reference and new ideas for the development of interior SQ in PEVs.

A novel optimization-based method to find multiple solutions for path synthesis of planar four-bar and slider-crank mechanisms

The classical method to find possible solutions for path synthesis problem of planar mechanisms is continuation method. However, this method has some disadvantages such as producing unwanted extraneous and degenerate solutions and also producing mechanisms having defects. Moreover, many of the solutions are cognate of each other which can be obtained geometrically. Thus, finding the most feasible solution among all solutions is a cumbersome and time-consuming task. The main purpose of this paper is to explore applicability of heuristic algorithms to find multiple cognate- and defect-free solutions for path synthesis problems of planar four-bar and slider-crank mechanisms. To this aim, a new modified error function and an optimization-based algorithm is presented. The gravitational search algorithm (GSA) is utilized to minimize the modified error function. Efficiency of the method is proved through five case studies for path synthesis of four-bar and slider-crank mechanisms with and without prescribed timing.