The hand trajectory of motion during the performance of one-dimensional point-to-point movements has been shown to be marked by motor primitives with a bell-shaped velocity profile. Researchers have investigated if motor primitives with the same shape mark also complex upper-limb movements. They have done so by analyzing the magnitude of the hand trajectory velocity vector. This approach has failed to identify motor primitives with a bell-shaped velocity profile as the basic elements underlying the generation of complex upper-limb movements. In this study, we examined upper-limb movements by analyzing instead the movement components defined according to a Cartesian coordinate system with axes oriented in the medio-lateral, antero-posterior, and vertical directions. To our surprise, we found out that a broad set of complex upper-limb movements can be modeled as a combination of motor primitives with a bell-shaped velocity profile defined according to the axes of the above-defined coordinate system. Most notably, we discovered that these motor primitives scale with the size of movement according to a power law. These results provide a novel key to the interpretation of brain and muscle synergy studies suggesting that human subjects use a scale-invariant encoding of movement patterns when performing upper-limb movements.