Position analysis of higher-class Assur groups by virtual variable searching and its application in a multifunction domestic sewing machine

Abstract

This paper presents a simple and effective method to solve the position of higher-class Assur groups by means of virtual variable searching. It transforms the higher-class Assur groups into a constraint link, Class II Assur group(s), and virtual driving link(s), defined by the virtual variable. The constraint link is reassembled by one-dimensional searching of the virtual variable, and the potential solutions of the position of the higher-class Assur group are achieved with rapid mathematic convergence. Detailed criteria are set up for complicated higherclass Assur groups, including how to select the virtual driving link and constraint Link, and how to decide the solving sequence of converted Class II Assur groups. A versatile visual program has been developed to simulate higher-class planar mechanisms. Finally, an example of the feeding mechanism of a multifunction domestic sewing machine demonstrates the new method.

Analytical method for the kinetostatic analysis of the second-class RRR Assur group allowing for friction in the kinematic pairs

“…Kinematics of mechanisms by a kinematic unit GP approach is reported by : Cavic, Kostic and Zlokolica (2007), who present an iterative method for the forward kinematics of high-class Assur groups by decomposing it into dyadic (second-class) forms; Zhang, Zou and Guo (2006), who develop a virtual searching method for the position analysis of higher-class Assur groups; Buśkiewicz (2006), who presents a general and optimal numerical method to calculate the kinematics of a mechanism when its structural classification is given; Mitsi, Bouzakis and Mansour (2004), Mitsi et al (2003) and Mitsi (1999), who develop a position analysis in polynomial form of Assur groups of class 4 and 3 including some prismatic joints; Calle, Quintero and Díaz (2001), who research a modular approach for the kinematic analysis of mechanisms; and Han, Liao, and Liang (2000), who analyze the position of a eightlink Assur group using a vectorial technique.…”