A Variational Approach for the Design of Spatial Four-Bar Mechanism*

Abstract

An analytical formulation for computing kinematic sensitivity of the spatial four-bar mechanism is presented. The experimental code developed is used to compute an assembled configuration for the mechanism due to a design variation. The mechanism is modeled using graph theory where a body is defined as a node and a kinematic joint is defined as an edge. The spherical joint is cut to convert the model into a tree structure by cutting an edge and introducing constraints. The effect of variation in mechanism design using concepts of virtual displacement and rotation is introduced. The variation of the spherical constraint is computed while maintaining joint-attachment vectors and orientation matrices as variables. A system of equations that has more design variables than equations is then solved using the modified Moore-Penrose pseudo inverse. A recursive formulation is introduced to obtain the state variation of a body in terms of the state variation of a junction body and of the relative coordinates along the chain. The Jacobian matrix is then transformed from Cartesian coordinate space to joint coordinate space using velocity transformation matrices. Kinematic sensitivity analyses due to changing a jointattachment vector and an orientation are presented.

Force analysis of bearings on a modified mechanism using proposed recurrent hybrid neural networks

“…x 1 (t+1)=W I1 u(t+1)+β x 1 (t)+αJ 1 y(t) (1) x 2 (t+1)=F{W I2 u(t+1)+β x 2 (t)+αJ 2 y(t)} (2) y(t+1)=W H1 x 1 (t+1) + W H2 x 2 (t+1)…”

“…Recently, an analytical formulation for computing kinematic sensitivity of the spatial four-bar mechanism has been described in [1]. An experimental code developed was used to compute an assembled configuration for the mechanism that accounts for the effect of a design variation.…”

Interactive Mechanical Design Variation for Haptics and CAD

“…The universal joint included here incorporates a spherical joint constraint for the first three constraints and a perpendicular constraint for the fourth equation. The universal joint features of the two bodies must meet, which is enough for a spherical joint constraint, given by C sph q = Aq i;rot k i + q i;disp ,Aq j;rot k j ,q j;disp 3x1 (9) A is a rotation matrix, q i;disp is a translation vector, and q i;rot are the rotation coordinates, whether Euler angles, quaternions, Rodriguez parameters, etc., and k is a constant local body frame vector indicating the position of the universal joint feature.…”

Number Synthesis of Parallel Robotic Mechanisms

“…The research on type synthesis of planar and special mechanisms (Joo and Kota, 2004;Mruthyunjaya, 1984a,b,c;Pucheta and Cardona, 2008;Zou et al, 1997) has been a hot topic in the international mechanisms and robotics research area. As a kind of knowledge-intensive mechanisms, type synthesis of parallel mechanisms (Hunt, 1978) is a complex and challenging problem.…”