For　the　angle　tracking　control　problem　of　free　floating　three　bar　space　manipulator　with　disturbance　torque　and　joint　dead　zone,　non　singular　fast　terminal　sliding　mode　fuzzy　adaptive　control　is　adopted　to　realize　finite　time　stabilization　of　tracking　error.　In　this　method,　a　nonsingular　fast　terminal　sliding　surface　is　used　to　make　the　state　variables　converge　rapidly　in　the　sliding　phase;　The　improved　double　power　reaching　law　is　selected　to　improve　the　convergence　speed　of　state　variables　in　the　approaching　motion　stage,　and　fuzzy　control　is　used　to　eliminate　chattering　and　improve　the　control　accuracy.　At　the　same　time,　considering　the　dead　time　characteristics　and　disturbance　torque　of　the　manipulator　joint,　an　adaptive　compensator　is　designed　to　approach　the　upper　bound　of　the　dead　time　characteristics　through　adaptive　control,　so　as　to　ensure　the　effective　implementation　of　the　tracking　control.　Finally,　based　on　Lyapunov　method,　the　global　stability　of　the　closed-loop　system　is　proved　theoretically,　and　the　numerical　simulation　shows　that　the　controller　can　effectively　realize　the　task　space　path　tracking　control,　effectively　improve　the　trajectory　tracking　accuracy　and　anti　disturbance　ability,　and　alleviate　the　chattering　phenomenon　in　the　output　of　the　controller.　©　2021,　Springer　Nature　Switzerland　AG.