This　study　presents　the　efficient　rigid-body　inverse　dynamics　of　a　spatial　parallel　mechanism　(PM)　constrained　directly　by　the　base　at　two　point-contact　higher　kinematic　pairs　(HKPs).　The　mechanism　is　designed　to　mimic　the　human　masticatory　system　and　is　characterised　by　these　constraints,　from　which　parasitic　motions　and　actuation　redundancies　are　derived　simultaneously.　At　the　beginning,　its　constrained　motions　are　analysed　comprehensively.　Then　to　seek　efficient　approaches　to　inverse　dynamics　and　the　influence　of　constraints　at　HKPs,　three　models　are　built　using　the　Udwadia-Kalaba　analytical　mechanics　method.　In　the　first　model,　a　dynamic　model　free　of　constraints　from　both　the　base　and　the　chains　to　the　end-effector　is　built　first,　and　then　these　constraints　are　formulated　to　reach　the　complete　dynamic　model　of　the　PM.　In　the　second　model,　a　dynamic　model　free　of　constraints　only　from　the　chains　to　the　end-effector　is　built　first,　and　then　these　constraints　are　imposed,　achieving　the　complete　dynamic　model　of　the　PM.　Whilst　in　the　third　one,　a　dynamic　model　free　of　only　direct　constraints　from　the　base　to　the　end-effector　is　built　first,　and　then　these　constraint　forces　are　developed　to　arrive　at　the　model　of　the　PM.　The　results　show　that　the　second　model　is　the　most　time-consuming.　However,　the　first　and　third　models　can　significantly　reduce　the　computational　complexity　without　any　accuracy　loss,　which　is　even　comparable　to　that　of　the　PM＇s　counterpart　free　of　direct　constraints　from　the　base　to　the　end-effector.