Theoretical study of kinematic pairs «torus with torus» based on geometric kinematics

Abstract

The article presents a theoretical study of kinematic pairs known as «rolling pairs» used in many areas of mechanical engineering, in particular, mechanisms. The research concerns such bodies (links) as geometric tori, which are well-known bodies of rotation. From the geometric kinematics, new representations of the mechanical motions of a torus in a «torus-torus» connection are described without the reasons that cause this motion. Two options for connecting two tori are analyzed: the axes of the tori are parallel and perpendicular. By analogy, the analysis of kinematic pairs of this type expands the elements of kinematic pairs theory and allows developing their new variants in many mechanisms used in various fields of mechanical engineering.

Keywords

• kinematic pair
• rolling pair
• torus
• mobility
• mobility matrix
• sliding
• rolling
• spinning