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.　©　The　Author(s),　2025.