Extending screw theory for analysing mechanisms incorporating higher kinematic pairs

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Abstract Screw theory serves as an influential mathematical tool, significantly contributing to mechanical engineering, with particular relevance to mechanism science and robotics. The instantaneous screw and the finite displacement screw have been used to analyse the degree of freedom and perform kinematic analysis of linkage mechanisms with only lower pairs. However, they are not suitable for higher pair mechanisms, which can achieve complex motions with a more concise structure by reasonably designing contact contours, and they possess advantages in some particular areas. Therefore, to improve the adaptability of screw theory, this paper aims to analyse higher kinematic pair (HKP) mechanisms and proposes a method to extend instantaneous screw and finite displacement screw theory. This method can not only analyse the instantaneous degree of freedom of HKP mechanisms but also determine the relationships between the motion variables of HKP mechanisms. Furthermore, this method is applied to calculate the degree of freedom and the relationships between the motion angles in both planar and spatial cam mechanisms, thereby demonstrating its efficiency and advantages.

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