A　life-sized　spatial　redundantly　actuated　parallel　mechanism　(RAPM)　constrained　by　two　point-contact　higher　kinematic　pairs　(HKPs)　has　been　designed,　inspired　by　the　mastication　of　human　beings.　To　facilitate　its　real-time　control　in　practice,　an　accurate　inverse　dynamics　model　is　built　in　this　paper.　Firstly,　its　constrained　motions　are　described,　thereafter　three　dynamics　methods,　i.e.,　Newton　-Euler＇s　law,　the　Lagrangian　equations　and　the　principle　of　virtual　work,　respectively,　are　used　to　explore　its　rigid-body　inverse　dynamics.　Symbolic　results　show　that　model　structures　based　on　these　approaches　are　quite　different.　The　model　via　Newton-Euler＇s　law　well　reflects　the　nature　of　the　mechanism　in　terms　of　the　constraint　forces　at　HKPs,　while　those　from　the　latter　two　methods　do　not　contain　them.　Despite　this,　the　actuating　torques　from　these　three　models　are　identical.　The　comparisons　between　the　dynamics　models　of　the　RAPM　and　its　counterpart　free　of　HKPs　clarify　that　the　constraints　at　HKPs　greatly　alter　the　model　structures　and　numerical　results,　and　the　computational　difficulties　are　considerably　larger　in　the　models　of　the　RAPM.