Dynamics analysis of a parallel hip joint simulator with four degree of freedoms (3R1T)

Unified solving inverse dynamics of 6-DOF serial–parallel manipulators

“…The input joint velocities of lower and upper PMs v n1 and v n2 can be derived based on the results of single limited-DOF PM as follows [22] v ni ¼ J ai…”

“…Velocity and Jacobian of whole of S-PM The velocities of r ij (i = 1, 2, 3) for single PM has been derived [22] and can be expressed as following …”

“…The accelerations of r ij (i = 1, 2; j = 1, 2, 3) for single PM has been derived and can be expressed as follows [22] a ni ¼ …”

“…For the dynamics, several approaches including Lagrange method, the Newton-Euler method, the principle of virtual work, the screw theory, etc [19][20][21][22] have been commonly applied. All approaches derive equivalent dynamic equations, although these equations present different levels of computational complexity.…”

Dynamic Modeling of a 2-RPU+2-UPS Hybrid Manipulator for Machining Application

“…While dynamic approaches, including the Lagrange method (Liu and Yu (2008), Wu et al (2014)), Newton-Euler method (Jalón and Bayo (1994), Zhang et al (2009)), Kane method (Cheng and Shan (2012)), principle of virtual work (Sokolov and Xirouchakis (2007)) and (Zhao et al (2009)), and screw theory (Gallardo-Alvarado et al (2008)) are commonly used and applied in manipulator dynamics (Horn and Linge (1995), Wu and Bai (2016)), this work adopts the principle of virtual work, under the consideration to eliminate the internal forces and effectively reduce the computational complexity.…”