To　improve　the　space　free　curve　trajectory　planning　accuracy　of　manipulators,a　new　trajectory　planning　algorithm　for　the　manipulators＇　position　planning　and　orientation　planning　is　presented.　The　one　to　one　mapping　from　position　and　orientation　points　in　3D　space　to　elements　of　double　quaternion　space　is　constructed　though　making　the　torch＇s　position　and　orientation　points　is　equivalent　to　the　points　in　the　double　quaternion　space,　Thus　the　problem　of　interpolation　of　torch＇s　position　and　orientation　points　is　transformed　to　the　problem　of　the　curve　interpolatory　in　the　double　quaternion　space.　Base　on　the　spherical　linear　interpolation　theory　of　quaternion　and　the　recursive　algorithm　of　Bezier　curve,　a　Bezier　interpolation　curve　of　double　quaternion　is　obtained　by　which　the　trajectory　curve　of　position　and　orientation　of　the　welding　torch　was　solved.　Simulations　show　that　the　presented　algorithm　can　effectively　complete　a　smooth　adjustment　for　position　and　orientation　trajectory　of　the　robot　welding　torch　and　provide　a　theoretical　basis　for　the　off-line　programming　and　movement　control　of　the　free　curve　and　surface　welding　of　the　welding　robot.　©,　2014,　Shanghai　Jiao　Tong　University.　All　right　reserved.