About Dual Spherical Wrist Motion and Its Trajectory Surface as a Ruled Surface

Solid object rotations or rotations of unit real vectors are often used in robotic moves. Yet, due to the complexity of calculations in kinematics analysis, quaternions began to be used in robotic moves. Quaternions help us to calculate rotations in reel space, and rotation and translation in dual space. Furthermore, we can easily define a screw or an axis through dual vectors. In recent years, there has been efficient studies in mechanics analysis by using dual quaternions and screw moves. In this study, we transferred the well known sequential and modular methods for the rotations being formed in real spherical wrist moves to dual space. Hence, while we rotate the unit vectors only in real space, now we can rotate screws .Hence, while we rotate the unit vectors only in real space, now we can rotate screws or the axis in the dual spherical mechanisms in dual kinematics. Through this study, by being switched to dual spherical mechanism the first time, we will see that we can carry out what we do with unit vectors in real space as well as in dual space. Furthermore, while the orbits drawn by the joint moves are curves in reel spherical wrist moves, the orbits drawn by the joint moves are ruled surfaces in dual spherical wrist moves. We think that this situation would establish a base for different mechanics studies.