Re-analysis of the degree-of-freedom configuration of the platforms in spatial parallel mechanisms with constraints spaces

The degree-of-freedom (DoF) configuration of a mechanism, which is an important concept in the field of mechanisms and is the key problem to be solved before mechanisms are designed, has been discussed in our previous article [1]. In this paper, we will further analyze the DoF configuration of the platforms of spatial parallel mechanisms with constraints spaces. According to the physical meaning of reciprocal screws, we can solve the constraints spaces spanned by reciprocal screws, and then solve the free mobility spaces of the platform and its DoF configuration. With this methodology, not only can we differentiate the system from its members, but we also extend the concept of DoF configuration, which should have the attributes of number, type, and direction.