Dynamic modeling of a parallel manipulator(PM) is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the global dynamic model of the PM system becomes increasingly prominent. Currently there lacks further research in global dynamic modeling. A unified modeling approach for the multi-energy domains PM system is proposed based on bond graph and a global dynamic model of the 3-UPS/S parallel stabilized platform involving mechanical and electrical-hydraulic elements is built. Firstly, the screw bond graph theory is improved based on the screw theory, the modular joint model is modeled and the normalized dynamic model of the mechanism is established. Secondly, combined with the electro-hydraulic servo system model built by traditional bond graph, the global dynamic model of the system is obtained, and then the motion, force and power of any element can be obtained directly. Lastly, the experiments and simulations of the driving forces, pressure and flow are performed, and the results show that, the theoretical calculation results of the driving forces are in accord with the experimental ones, and the pressure and flow of the first limb and the third limb are symmetry with each other. The results are reasonable and verify the correctness and effectiveness of the model and the method. The proposed dynamic modeling method provides a reference for modeling of other multi-energy domains system which contains complex PM.
The determination of virtual constraints is always one of the key and difficult problems in traditional mobility calculation.To make mobility calculation simple,considering avoiding virtual constraints,some new formulae have been presented,however these formulae can hardly intuitively reflect general link group’s restrictions on output member and its influences on independence of output parameters,which is premise to the judgment of the properties of mobility.Towards the problem to reveal the intrinsic relationship between the degree of freedom(DOF)of a mechanism,the link group,and the dimension of output parameters,also to avoid determination of virtual constraint,based on the new concepts of the"DOF of general link group"and"node parameters",a new formula in the calculation of the mobility of mechanisms is presented that is expressed with DOFs of the general link groups and rank of motion parameters of base point of the output link.It is named GOM(mobility of groups and output parameter)formula.On the basis of new concepts of"effective parameters"and"invalid parameters",a rule is put forward for solving the DOF of mechanisms with invalid parameters by GOM formula,that is,the base point parameters are the subset of effective parameters of link group.Thereafter,several examples are enumerated and the results coincide with the prototype data,which proves the validity of the proposed formula.Meanwhile,it is obtained that the necessary and sufficient condition for the judgment of output parameters independence is that each of the DOF of the link group is not less than zero.The proposed formula which is simple in calculation provides theoretical basis for the judgment of independence of output parameters and provides references for type synthesis of novel parallel mechanisms with independence requirements of their output parameters.
