To tackle the challenge of planning coordinated movements between robots and positioners during robot-assisted 3D measurement, we propose a robot–positioner collaborative scanning motion planning method based on the geometric relationships of four key points. Using four points—the turntable center A, the scanner center B, the robot base C, and the positioner base D—we construct a fixed main plane and a dynamic probe plane. Candidate positioner angles are geometrically pre-screened using lateral position relationships and plane deviation angles. Following the principle of ''robot first, positioner support,'' the positioner’s zero position is preferred, and angle searching is initiated only if geometric pre-screening or reachability verification fails. For continuous scanning paths, a unified positioner angle is chosen to reduce turntable switches. Simulations on typical complex surface parts show that this method is quite feasible. In experiments with 12 scanning viewpoints, the planned trajectories achieved a 100% success rate for inverse kinematics and collision checks, with a scan coverage of 82.13%. This approach efficiently plans positioner angles and ensures smooth transitions for continuous trajectories while maintaining scan coverage and path executability.