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The procedure of modeling planar linkage containing translational joint by vector bond graphs is described. 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, most of the differential causalities in system vector bond graph model can be eliminated. Based on this, the unified formulae of system state space equations and constraint forces at joints are derived, 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. This procedure is very suitable for the modeling and simulation of the systems containing multi-energy domains in a unified manner, its validity is illustrated by a practical example.