Based　on　the　previous　research　studies,　the　analytical　formula　of　the　optimal　joint　velocity　with　minimum　jump　for　robots　with　multi-degrees　of　redundancy　is　derived.　This　new　algorithm　considers　the　motion　planning　of　healthy　and　reduced　robots　at　the　same　time　to　achieve　an　overall　better　performance　of　fault　tolerance.　Simulation　examples　are　implemented　with　a　planar　4　R　robot　and　a　5　R　spatial　robot.　In　the　end,　the　issues　of　reducing　the　joint　velocity　jump　and　thereby　improving　the　motion　stability　for　both　single-degree　and　multi-degree　redundant　robots　in　fault-tolerant　operations　are　completely　solved.