The　motion　state　of　balls　in　the　ball　screw　mechanism　is　hard　to　observed　or　measured　because　of　the　complexity　of　the　mechanism　consisting　of　three　main　components:　screw,　nut　and　balls.　In　this　paper,　a　kinematic　model　for　the　basic　single　arc　ball　screw　mechanism　driven　by　the　rotation　of　the　screw　is　established　using　the　homogenous　transformation　matrix,　and　the　kinematic　characteristics　and　slide-roll　ratios　at　contact　points　of　the　raceways　are　analyzed.　There　are　five　possible　relative　motion　states:　a)　screw　pure　rolling　and　nut　rolling-sliding　mixed　motion,　b)　nut　pure　rolling　and　screw　rolling-sliding　mixed　motion,　c)　screw　pure　sliding　and　nut　no　relative　motion,　d)　nut　pure　sliding　and　screw　no　relative　motion,　and　e)　both　rolling-sliding　mixed　motion　between　the　balls　and　the　raceways　of　the　screw　and　nut　in　the　tangential　direction　of　the　helix　path.　A　parametric　study　is　also　carried　out　to　evaluate　the　effect　of　motion　velocity　on　the　slide-roll　ratio　based　on　the　numerical　calculations　of　the　slide-roll　ratio　at　the　contact　points.　(C)　2014　Elsevier　Ltd.　All　rights　reserved.