Is the principle of minimization of secondary moments validated during various fingertip force production conditions?

During the application of fingertip forces with simultaneous flexion of the four fingers, namely index, middle, ring, and little fingers, a stable force sharing among fingers is adopted. Several studies have hypothesized that this stable force sharing is established to minimize unnecessary rotational moments (different from the main flexion moments). This principle labeled "minimization of secondary moments" is presented in the literature as a principle used by the central nervous system to solve musculoskeletal redundancy. However, this principle has only been tested with one solicited degree of freedom and in one finger posture. Our study tests this principle with various degrees of freedom solicited as secondary moments and in two different finger postures. Participants (n=6) were asked to apply a downward vertical force using their four fingers with the forearm placed in two different configurations: a "horizontal" condition (involving flexion/extension and pronation/supination at the wrist joint) and a "vertical" condition (involving flexion/extension and radial/ulnar deviation at the wrist joint). Additionally, two finger postures were tested in each forearm configuration: in the first, the distal inter-phalangeal joints (DIP) were extended and the proximal inter-phalangeal joints (PIP) highly flexed. In the second finger posture, both DIP and PIP joints were flexed. The resultant four-finger force and the relative involvement of each finger in the resultant four-finger force (force sharing) were analyzed. Results showed that the finger postures did not influence the finger force sharing, showing that the minimization of the secondary moment principle was stable among the finger joint angle configurations. Nonetheless, the relative involvement of each finger was dependent on the secondary degree of freedom solicited (pronation/supination vs. radial/ulnar). The modifications of the finger force sharing between the "horizontal" and "vertical" conditions were in accordance with the principle of minimization of the secondary moments.