This paper presents a composite modeling method of the forward dynamics in general planar mechanical system. In the modeling process, the system dynamic model is generated by assembling the model units which are kinematical determinate in planar mechanisms rather than the body/joint units in multi-body system. A state space formulation is employed to model both the unit and system models. The validation and feasibility of the method are illustrated by a case study of a four-bar mechanism. The advantage of this method is that the models are easier to reuse and the system is easier to reconfigure. The formulation reveals the relationship between the topology and dynamics of the planar mechanism to some extent.
The dynamics analysis plays an important role for the control,simulation and optimization of the parallel manipulators. Normally,the Stewart type manipulators have a platform and several legs. The inverse dynamics can be solved efficiently by taking the advantage of such structural characteristics. However,for the forward dynamics analysis,this structural decomposition still faces challenges from both modeling and computation. In this paper,an efficient approach is proposed for the forward dynamics of the 6-PUS manipulator based on the platform-legs composite simulation. By composite method,the dynamics modeling of the parallel manipulator is separated into the forward dynamics of the platform and the kineto-statics of the legs. The global simulation model can be constructed by connecting the predefined platform model and leg models according to the manipulator's topology. Thus,the global simulation can be decomposed into the independent calculations of purely algebraic equations and ordinary differential equations (ODEs),the computational cost can be reduced and the stability of the simulation can be improved. For the purpose of solving the manipulator's forward dynamics accurately,the algebraic-loop problem is discussed and a closed form algorithm is proposed. A numerical example of the 6-PUS manipulator is given to demonstrate the effectiveness of the proposed approach. The example results show that the modeling efficiency can be improved and the simulation stability can be ensured for decomposing the system equations into purely algebraic equations and ODEs.
