In　order　to　solve　the　joint　tracking　control　and　vibration　problem　of　flexible-joint　space　robot　system　in　the　pre-grasping　stage　when　the　position　and　pose　are　not　controlled,　the　dynamic　equations　of　a　free-floating　three-bar　flexible-joint　space　robot　system　are　established　using　the　Lagrangian　equation　in　conjunction　with　the　principle　of　momentum　conservation.　In　order　to　improve　the　equivalent　stiffness　of　flexible-joint,　a　joint　flexible　compensation　method　was　introduced.　The　flexible-joint　space　robot　system　was　divided　into　slow　and　fast　systems　by　singular　perturbation　theory.　On　this　basis,　a　sliding　mode　control　method　with　time　delay　estimation　as　the　main　framework　was　designed　for　the　slow　variable　systems,　while　combining　it　with　a　low-pass　filter　to　eliminate　the　system　chattering　problem　caused　by　sliding　mode　control.　A　linear　velocity　difference　feedback　control　system　was　designed　for　the　fast-changing　system　to　suppress　the　flexible　vibration　problems　introduced　by　the　flexible　joints.　Simulation　verification　demonstrates　that　the　space　robotic　arm　is　capable　of　quickly　and　steadily　tracking　the　desired　trajectory　within　a　limited　time,　confirming　that　the　control　scheme　possesses　good　robustness　and　reliability.　©　2024　National　University　of　Defense　Technology.　All　rights　reserved.