This study investigates unrestrained vertical arm movements between point targets using a three-dimensional tracking system, the Selspot system. The researchers found that, contrary to previous findings emphasizing straight hand paths, some movements exhibited curved paths. However, all movements, whether straight or curved, showed an invariant tangential velocity profile when normalized for speed and distance. This velocity profile invariance is interpreted as a simplification of the underlying arm dynamics, extending previous results by Hollerbach and Flash (1982). The study also examines the effects of different loads and gravity on arm trajectories. The results indicate that trajectory shape and tangential velocity profile are invariant across different conditions of speed, load, path, and subject. This invariance suggests that subjects execute only one form of trajectory between any two targets, with changes in speed accommodated by simple scaling operations. The dynamic scaling properties for speed and load are discussed, and the authors propose a model where the motor controller separates gravity torques from dynamic torques and scales the tangential velocity profile uniformly. The study concludes that the invariance of the tangential velocity profile and the dependence of path curvature on movement direction are new findings. The authors suggest that these results may be explained by the naturalness of vertical movements and the compliant nature of horizontal planar movements. They also discuss the implications of these findings for understanding the control strategies used by the motor system.This study investigates unrestrained vertical arm movements between point targets using a three-dimensional tracking system, the Selspot system. The researchers found that, contrary to previous findings emphasizing straight hand paths, some movements exhibited curved paths. However, all movements, whether straight or curved, showed an invariant tangential velocity profile when normalized for speed and distance. This velocity profile invariance is interpreted as a simplification of the underlying arm dynamics, extending previous results by Hollerbach and Flash (1982). The study also examines the effects of different loads and gravity on arm trajectories. The results indicate that trajectory shape and tangential velocity profile are invariant across different conditions of speed, load, path, and subject. This invariance suggests that subjects execute only one form of trajectory between any two targets, with changes in speed accommodated by simple scaling operations. The dynamic scaling properties for speed and load are discussed, and the authors propose a model where the motor controller separates gravity torques from dynamic torques and scales the tangential velocity profile uniformly. The study concludes that the invariance of the tangential velocity profile and the dependence of path curvature on movement direction are new findings. The authors suggest that these results may be explained by the naturalness of vertical movements and the compliant nature of horizontal planar movements. They also discuss the implications of these findings for understanding the control strategies used by the motor system.