The minimum number of muscles to control a chain of joints with and without tenodeses, arthrodeses, or braces—application to the human finger

While the underlying principles of controlling a single joint have been well described, the principles of simultaneously controlling multiple joints have not been comprehensively addressed in the literature of reconstructive hand surgery. This article analyzes (1) how many muscles are minimally required to fully control a chain of joints with in total N Degrees of Freedom (DoF), and (2) to what degree tenodeses, arthrodeses or braces can reduce the required number of muscles. It is demonstrated by mathematical analysis and illustrated by examples that the minimal number of muscles to control a chain of N DoF is N+1. The number of muscles required for control can be reduced by mechanisms that reduce the number of DoF in the chain. (i) An arthrodesis is a permanent surgical fixation of a joint. An arthrodesis eliminates as many DoF in the chain as the arthrodized joints contributed. (ii) Tenodeses are coordinative tendon constructions. Each independent tenodesis eliminates one DoF from the chain. (iii) Braces are removable external supports. They eliminate as many DoF for muscle control as they immobilize. These principles are applied to illustrate the fundamental importance of tendinous structures in control in the human finger. Being able to determine the minimum number of muscles needed for multiarticular control gives additional knowledge in the design of functional reconstruction.