It　has　remained　a　great　challenge　to　develop　coupled　mechanisms　in　kinematics.　Polyhedrons　with　various　appearance　and　symmetric　configuration　attract　more　and　more　attentions　and　provide　possible　basic　modes　for　the　design　of　coupled　mechanisms.　Based　on　the　symmetry　and　duality　of　the　regular　dodecahedron,　a　movable　icosahedron　mechanism　with　single　mobility　was　designed,　where　the　coupling　nodes　were　composed　of　triangles,　quadrilaterals　and　pentagons.　Firstly,　in　order　to　design　the　coupling　nodes　with　triangles,　quadrilaterals　and　pentagons,　each　vertex　was　added　to　the　ten　faces　of　the　icosahedron　and　the　node　variety　was　increased　by　adding　types　of　vertexes.　The　common　edge　of　the　original　regular　pentagon　was　replaced　by　four　edges.　Four　edges　made　up　a　quadrilateral.　The　common　edge　of　the　original　regular　pentagon　became　a　diagonal　of　the　quadrilateral.　Then　four　kinds　of　replacement　components　were　designed　according　to　the　connection　of　each　component,　and　the　replacement　components　sequentially　were　connected　by　rotational　joints　to　construct　a　basic　model　of　the　coupled　mechanism.　Secondly,　mobility　of　the　mechanism　model　was　calculated　by　the　shunting　method　based　on　screw　theory.　The　coupled　mechanism　was　divided　into　five　identical　branches　according　to　the　shunting　tags.　As　long　as　the　constraints　of　one　branch　were　determined　based　on　screw　theory,　the　constraints　of　all　branches　to　the　moving　platform　was　obtained.　Then　mobility　of　the　coupled　mechanism　was　obtained,　which　showed　the　coupled　mechanism　had　a　translational　freedom.　Finally,　active　input　selection　was　analyzed　and　the　three-dimensional　model　of　the　coupled　mechanism　was　established.　Two　opposite　driving　conditions　were　set　up　in　the　simulation,　and　position　curves　of　the　moving　platform　and　the　node　components　were　got　by　Matlab.　The　simulation　results　were　consistent　with　theoretical　results.　It　further　showed　that　the　proposed　mechanism　had　the　characteristics　of　stretching　motion.　©　2017,　Chinese　Society　of　Agricultural　Machinery.　All　right　reserved.