The dynamic modelling and simulation of planar linkage containing translational joint based on vector bond graph

The dynamic modelling and simulation of planar flexible multibody systems based on vector bond graph

“…The constraint force vectors of joints can be y Fig.3 Crank-rocker mechanism considered as unknown source vectors, such as Se" Se lO, Sell ' Set2 in Fig.5, and added to the corresponding 0-junctions to eliminate differential causality caused by the geometric constraints between the bodies of the system. Thus the system dynamic equations and constraint force equations can be derived and solved automatically on a computer by the procedure in [7]. the system responses and the resultant forces at the joints are obtained and shown in Fig.5, Fig.6, Fig.7 and Fig.8.…”

“…But for the planar flexible linkage containing tranlational joint, most of the differential causality in system vector bond graph model can be eliminated. In [7], the unified formulae of system state space equations and constraint forces at joints are derived in the case of mixed causality, which are easily derived on a computer. As a result, the algebraic difficulty brought up by nonlinear junction structure and differential causality in automatic modelling and simulation can be solved .…”

A Vector Bond Graph Method of Kineto-Static Analysis for Complex Planar Linkage

“…To eliminate the differential causality of vector bond graph model presented in [5], the constraint force vectors at joints can be considered as unknown effort source vectors and added to the corresponding 0-junctions of the system vector bond graph model. For the planar linkage only containing revolute joint, the differential causality can be eliminated completely.…”

“…Compared with scalar bond graph [3] , vector bond graph is more suitable for modelling complex multibody systems because of its more compact and concise representation manner [4] . In [5], the procedure of modeling complex planar linkage containing slider joint by vector bond graphs is described. But for this vector bond graph model, the kinematic and geometric constraints between bodies result in differential causality loop, and the nonlinear velocity relationship between the mass center and an arbitrary point on a body leads to the nonlinear junction structure.…”

“…This is planar linkage containing two slider joint. By the procedure presented in[5], the vector bond graph of this mechanism can be obtained and shown in Fig.3. The constraint force vectors of joints can be considered as unknown source vectors, such as 2Se ,…”