Abstract:Analyzing mobility of parallel mechanisms digitally and automatically is the foundation of automatic type synthesis of parallel mechanisms. The mobility of parallel mechanisms was analyzed automatically based on R(3,3) geometric algebra model, which was a R6 geometric algebra model. Firstly, since any screw can be represented by a known screw with rigid body transformations, and the rigid body transformations can be derived by the geometric relationship between the two screws, when the twists of the first joints of the limbs were known, all twists of limbs of a parallel mechanism can be symbolically expressed and automatically computed by the geometric relationships between the joints of limbs. Then, since the motion of the limb was the union of all twists of joints and the motion of the moving platform was the intersection of all motion of limbs, by taking the advantages that the geometric algebra had the representations of the intersection set and union set, the motion of all limbs and the moving platform can also be symbolically expressed and automatically computed. Moreover, the symbolic expression of the motion of moving platform was exactly the moblity of the parallel mechanism. And the degree of a parallel mechanism was given by the blade of the symbolic expression. Finally, some examples were discussed in details by using the C++ coding to verify the proposed algorithm. The algorithm that analyzing the mobility of parallel mechanisms automatically based on geometric algebra did not need to compute the constraint twists of limbs and solve linear equations, which made this algorithm faster and more efficiency. This algorithm set the stage for automatic type synthesis of parallel mechanism.
