This　paper　presents　a　comparative　study　of　the　rigid-body　inverse　dynamics　of　a　spatial　redundantly　actuated　parallel　mechanism　constrained　by　two　point　contact　higher　kinematic　pairs　(HKPs).　Firstly,　its　constrained　motions　are　analysed　comprehensively,　then　four　different　models　are　formulated　by　the　generalized　momentum　approach　and　the　Lagrange-D＇Alembert　formulation　to　explore　its　inverse　dynamics.　In　each　method,　the　first　model　is　built　by　employing　the　method　directly　to　the　mechanism.　In　the　second　model,　the　dynamic　model　of　its　non-redundantly　actuated　counterpart　free　of　HKPs　is　built　by　this　approach　first,　then　the　constraints　from　HKPs　are　modelled,　to　finally　reach　the　model　of　the　redundantly　actuated　parallel　mechanism　(RAPM)　where　that　of　its　counterpart　is　utilised　as　the　core.　The　four　models　give　rise　to　equivalent　numerical　results,　and　the　second　model　in　both　methods　of　the　RAPM　can　alleviate　the　strong　coupling　between　the　parasitic　motion　variables　and　degrees　of　freedom　(DOFs),　boosting　the　computational　speed　as　fast　as　that　of　its　non-redundantly　actuated　counterpart　without　simplification　or　loss　of　accuracy.　The　comparisons　between　the　mechanism　and　its　counterpart　validate　that　the　HKP　constraints　greatly　increase　the　computational　complexity,　and　the　torques　required　by　the　parasitic　motions　of　the　end　effector　are　significantly　smaller　than　those　by　the　corresponding　DOFs.