Recursive　matrix　relations　concerning　the　kinematics　and　the　dynamics　of　a　constrained　robotic　system,　schematized　by　several　kinematical　chains,　are　established　in　this　paper.　Introducing　frames　and　bases,　we　first　analyze　the　geometrical　properties　of　the　mechanism　and　derive　a　general　set　of　relations.　Kinematics　of　the　vector　system　of　velocities　and　accelerations　for　each　element　of　robot　are　then　obtained.　Expressed　for　every　independent　loop　of　the　robot,　useful　conditions　of　connectivity　regarding　the　relative　velocities　and　accelerations　are　determined　for　direct　or　inverse　kinematics　problem.　Based　on　the　general　principle　of　virtual　powers,　final　matrix　relations　written　in　a　recursive　compact　form　express　just　the　explicit　dynamics　equations　of　a　constrained　robotic　system.　Establishing　active　forces　or　actuator　torques　in　an　inverse　dynamic　problem,　these　equations　are　useful　in　fact　for　real-time　control　of　a　robot.