DUAL QUATERNION CLOSED FORM EQUATIONS OF SPATIAL 7R LOOPS

*F.H. MAMMADOV (pp. 38-52)*

#### Abstract.

By using the double quaternions, 16 finite-form algebraic equations are derived that express the conditions for the closure of the 7R mechanism. It was possible to significantly simplify these equations by introducing intermediate angles. The unknowns are sines and cosines of intermediate angles, which are linear combinations of output angles of rotation in kinematic pairs. The first six equations of the 16 are linear with respect to the unknowns, the following 8 equations express the equality to unity of the sum of squares of sines and cosines, and the remaining 2 equations express additional connections between the unknowns. Numerical results are obtained.#### Keywords:

quaternions, dual numbers, manipulator, space transformations, kinematic analysis.