Metamorphic mechanism has the advantages of variable topology and variable degrees of freedom, which can realize the requirements of multi-conditions and multi-tasks, and has a good application prospect. The configuration transformation is prominent feature of the metamorphic mechanism. The number of constraints or properties of the kinematic pairs provided by the metamorphic kinematic pairs will change under certain conditions, its dynamic performance is much more complex than that of traditional kinematic pairs with immutable constraints. However, the clearance model about traditional kinematic pairs with immutable constraints established by long-term research is difficult to be directly applied to the metachromatic kinematic pairs. Referring to the experience of the traditional kinematic pairs with immutable constraints, the continuous contact model of Metamorphic Groove pin pair with clearance is established. According to the traditional continuous contact model of the kinematic pairs with immutable constraints, the forces between the elements of kinematic pair of the mechanism with clearance and the ideal mechanism without clearance are regarded as the same, and the inertia force and inertia moment of the components are also calculated according to the acceleration of the ideal mechanism. The clearance is regarded as a massless virtual bar with length r. For the rotating pair part, the massless virtual bar length r is the difference between the radius of the shaft and the hole, and for the sliding pair part, the massless virtual bar length r is half of the difference between the height of the slider and the guide groove. According to the new mechanism without gap after adding the imaginary bar, kinetic energy and potential energy of the system are calculated for the two configurations of mechanism with metamorphic Groove pin pair with clearance. The kinetic energy and potential energy of the system are calculated according to the new mechanism without clearance after adding the massless virtual bar. The kinetic energy, potential energy and generalized force are substituted into the Lagrangian equation to obtain the motion equation of the metamorphic mechanism, which lays the foundation for the dynamic performance study of the mechanism with metamorphic groove pin pair with clearance.
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