The　inverse　kinematics　and　inverse　dynamics　of　the　3-DOF　Tricept　parallel　mechanism　with　redundant　actuation　are　analyzed.　The　inverse　dynamic　equation　of　the　mechanism　is　established　on　the　basis　of　Newton-Euler　approach.　For　the　character　that　the　distribution　of　the　active　joints＇　drive　forces　is　not　unique　due　to　the　redundant　actuation,　the　drive　optimization　for　the　mechanism　tracking　anticipant　trajectory　is　studied　and　the　methods　to　minimize　the　maximum　instantaneous　values　of　driving　power　and　driving　force　of　joint　actuators　are　proposed.　The　effectiveness　of　2-norm　optimizing　of　driving　force,　minimax　value　optimizing　of　driving　force　and　minimax　value　optimizing　of　driving　power　are　analyzed　by　means　of　several　examples,　and　are　compared　with　the　result　of　non-redundant　drive　mechanism.　The　analyses　indicate　that　the　redundant　actuation　can　evidently　reduce　the　instantaneous　drive　force　and　instantaneous　output　power　of　the　actuators,　and　based　on　the　contrastive　analysis　of　the　effectiveness　of　2-norm　optimizing　of　driving　force,　minimax　value　optimizing　of　driving　force　and　minimax　value　optimizing　of　driving　power,　the　appropriate　drive　method　can　be　chosen　to　optimize　and　equipoise　the　instantaneous　driving　force　and　instantaneous　output　power　of　the　actuators.　©　2010　Journal　of　Mechanical　Engineering.