A rigorous description of the magnitude and direction of the 3D force vector each thumb muscle produces at the thumb-tip is necessary to understand the biomechanical consequences to pinch of a variety of paralyses and surgical procedures (such as tendon transfers). In this study, we characterized the 3D force vector each muscle produces at the thumb-tip, and investigated if these thumb-tip force vectors scaled linearly with tendon tension. In 13 cadaver specimens, we measured the output 3D thumb-tip force vector produced by each tendon acting on the thumb, plus two common tendon transfers, as a function of input tendon tension. After fixing the hand to a rigid frame, we mounted the thumb by configuring it in standardized key or opposition pinch posture and coupling the thumb-tip to a rigidly held 6 degree-of-freedom force/torque sensor. Linear actuators applied tension to the distal tendons of the four extrinsic thumb muscles, and to six Nylon cords reproducing the lines of action of (i) the four intrinsic thumb muscles and (ii) two alternative tendon transfers commonly used to restore thumb opposition following low median nerve palsy. Each computer-controlled linear actuator ramped tendon tension from zero to 1/3 of predicted maximal muscle force expected at each tendon, and back to zero, while we measured the 3D force vector at the thumb-tip. In test/re-test trials, we saw thumb-tip force vectors were quite sensitive to mounting procedure, but also sensitive to variations in the seating of joint surfaces. We found that: (i) some thumb-tip force vectors act in unexpected directions (e.g., the opponens force vector is parallel to the distal phalanx), (ii) the two tendon transfers produced patently different force vectors, and (iii) for most muscles, thumb-tip force vectors do not scale linearly with tendon tension--likely due to load-dependent viscoelastic tendon paths, joint seating and/or bone motion. Our 3D force vector data provide the first quantitative reference descriptions of the thumb-tip force vectors produced by all thumb muscles and two tendon transfers. We conclude that it may not be realistic to assume in biomechanical models that thumb-tip force vectors scale linearly with tendon tensions, and that our data suggest the thumb may act as a "floating digit" affected by load-dependent trapezium motion.