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Type synthesis of two-degrees-of-freedom rotational parallel mechanism with two continuous rotational axes

The two-rotational-degrees-of-freedom(2R) parallel mechanism(PM) with two continuous rotational axes(CRAs) has a simple kinematic model. It is therefore easy to implement trajectory planning, parameter calibration, and motion control, which allows for a variety of application prospects. However, no systematic analysis on structural constraints of the 2R-PM with two CRAs has been performed, and there are only a few types of 2R-PM with two CRAs. Thus, a theory regarding the type synthesis of the 2R-PM with two CRAs is systematically established. First, combining the theories of reciprocal screw and space geometry, the spatial arrangement relationships of the constraint forces applied to the moving platform by the branches are explored, which give the 2R-PM two CRAs. The different distributions of the constraint forces in each branch are also studied. On the basis of the obtained structural constraints of branches, and considering the geometric relationships of constraint forces in each branch, the appropriate kinematic chains are constructed. Through the reasonable configuration of branch kinematic chains corresponding to every structural constraint, a series of new 2R-PMs with two CRAs are finally obtained.