Abstract: For the parallel mechanisms, there are multiple methods to describe the pose of the mobile platform. Different description methods will bring different effect on the kinematics analysis, so it is pretty important to select the appropriate description method. The mobile platform can be regard as the rigid body with constraints. As the different description methods of the rigid body have some internal relations, it is necessary to find the internal relations which will be useful to select the appropriate description method. When the mobile platform plane rotates a certain angle around one axis which is not normal to the plane, it will have a coupling angle around the normal of the plane, and this angle analytic expression is obtained. On the basis of the different description methods, the coupling angle around the normal and its analytic expression are identified after the rigid body successively rotating around two axes which lie in the mobile platform plane. The internal relations among the description methods are found; then aiming at the mobile platform with two rotational degrees of freedom, the reasonable selection principles are established. This conclusion applies to majority mobile platforms with two rotational degrees of freedom.

Key words: coupling angle, degree of freedom, parallel mechanism, pose description