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This paper presents a new trajectory generation algorithm for a space manipulator after capturing an uncooperative tumbling target. In particular, the previously developed Adaptive ReactionLess Control algorithm (ARLC) is extended to obtain minimum base reaction motion of the manipulator with consideration of joint limit constraints. A task-priority redundancy resolution technique is formulated within an adaptive control scheme with the primary task to maintain minimum disturbance to the base and the secondary task to avoid the physical joint limits. This control scheme is intended for use in the transition phase of the capture mission from the instant of capture till the unknown parameters are identified and/or the available post-capture stabilization methods can be applied properly. To verify the validity and feasibility of the proposed concept, MSC.Adams simulation platform is employed to implement a planar base-manipulator-target model as well as the three-dimensional model of Engineering Test Satellite VII system. The numerical results show that the proposed control scheme is able to generate the reactionless maneuver without violating joint limits of the arm, after capture of an unknown tumbling target.