This　paper　produces　a　C-space　layered　search　arithmetic　for　a　typical　of　manipulators　with　vertical　multi-joint　in　series.　The　work　divides　the　C　space　into　many　layers　based　on　the　dimension,　and　implements　the　rapid　creation　of　C-space　grid　map　on　each　layer.　After　generating　the　C-space　grid　map　of　the　first　layer,　the　system　searches　and　produces　the　C-space　grid　map　of　next　layer.　There　is　no　need　for　the　system　to　know　the　entire　C-space.　This　arithmetic　avoids　the　great　amount　of　the　calculation　and　the　large　demand　of　the　memory　space　of　C-space　grid　map　caused　by　the　dimensions　explosion　of　the　multi-joint　manipulator,　makes　sure　that　the　searching　processing　be　quick　and　complete.　©　2011　IEEE.