Position analysis in polynomial form of planar mechanism with an Assur group of class 4 including one prismatic joint

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.…”

Formulating Assur kinematic chains as projective extensions of Baranov trusses

“…The position analysis problem of the ten 5-link Assur kinematic chains was solved for the first time in closed form by Li and Matthew in [8]. Other solutions for 5-link Assur kinematic chains have been presented, at least, in [9,10,11,12,13]. An extensive research on the position analysis of Assur kinematic chains with only revolute joints, i.e.…”

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

“…However, their kinematic analysis -one of the most important aspects in linkage design -is still to be solved for more convenience and for greater effectiveness. And yet a lot of work has been done [2][3][4][5][6][7][8][9][10]. Kinematic analysis includes position analysis, velocity analysis and acceleration analysis; of these, position analysis is the most difficult.…”

“…Kinematic analysis includes position analysis, velocity analysis and acceleration analysis; of these, position analysis is the most difficult. To analyze the position of a complex planar linkage, there are two categories of methods: the global method [9,10] and the group method [2,[4][5][6][7][8]. The global method takes the linkage as a whole by listing the position equations based on the vector loop, and solving the equations using different techniques.…”