## Appendix A Direct Kinematic Model in Detail  
In this appendix, the direct kinematic model is presented in detail so the reader can see how it was solved step by step. Equations (A1) and (A2) describe the first kinematic chain in terms of its coordinates. \[r_{5}\cos\theta_{5}+r_{4}\cos\theta_{4} =r_{1}\cos\theta_{1}+r_{6}\cos\theta_{6}\] (A1) \[r_{5}\sin\theta_{5}+r_{4}\sin\theta_{4} =r_{1}\sin\theta_{1}+r_{6}\sin\theta_{6}\] (A2)  
Equations (A3) and (A4) describe the second kinematic chain. \[r_{5}\cos\theta_{5}+r_{7}\cos\theta_{7} =r_{1}\cos\theta_{1}+r_{2}\cos\theta_{2}+r_{8}\cos\theta_{8}\] (A3) \[r_{5}\sin\theta_{5}+r_{7}\sin\theta_{7} =r_{1}\sin\theta_{1}+r_{2}\sin\theta_{2}+r_{8}\sin\theta_{8}\] (A4)  
Vector \(\vec{R}_{3}\) represents the distal phalanx, while vector \(\vec{R}_{2}\) is the middle phalanx; thus if the parametric model is incorporated within the kinematic equations, then \(R_{2}\) can be represented as: \(r_{2}=1.4r_{3}\). Therefore, Equations (A3) and (A4) are rewritten as Equations (A5) and (A6). \[r_{5}\cos\theta_{5}+r_{7}\cos\theta_{7} =r_{1}\cos\theta_{1}+1.4r_{3}\cos\theta_{2}+r_{8}\cos\theta_{8}\] (A5) \[r_{5}\sin\theta_{5}+r_{7}\sin\theta_{7} =r_{1}\sin\theta_{1}+1.4r_{3}\sin\theta_{2}+r_{8}\sin\theta_{8}\] (A6) \[X^{\prime} =r_{1}\cos\theta_{1}+r_{3}(1.4\cos\theta_{2}+\cos\theta_{3})\] (A7) \[Y^{\prime} =r_{1}\sin\theta_{1}+r_{3}(1.4\sin\theta_{2}+\sin\theta_{3})\] (A8)  
Equations (A7) and (A8) describe the third kinematic chain. \[X_{d} =r_{3}(\cos\theta_{3}+1.4\cos\theta_{2})\] (A9) \[Y_{d} =r_{3}(\sin\theta_{3}+1.4\sin\theta_{2})\] (A10)  
Equations (A9) and (A10) describe the fourth kinematic chain. As it can be seen from Equations (A1) to (A10), there are equations in which two angles are unknown. Therefore, the middle angle theorem is used in order to solve for the unknowns. Initially, it may seem as if there are not enough equations to solve the system, but in reality, there are two constant relationships: one between angles \(\theta_{2}\) and \(\theta_{6}\) and another between \(\theta_{3}\) and \(\theta_{8}\). This relationship is defined by the mechanical design; it is fixed, and is represented by Equations (5) and (6). After performing the corresponding algebra and solving for all the unknowns, the following Equations (A11)-(A29) are obtained. \[r_{5}\sin\theta_{5}+r_{4}\sin\theta_{4} =r_{1}\sin\theta_{1}+r_{6}\sin\theta_{6}\]0 (A11)  
where \(A\), \(B\), \(C\) are given by:  
\[r_{5}\sin\theta_{5}+r_{4}\sin\theta_{4} =r_{1}\sin\theta_{1}+r_{6}\sin\theta_{6}\]1 (A12) \[r_{5}\sin\theta_{5}+r_{4}\sin\theta_{4} =r_{1}\sin\theta_{1}+r_{6}\sin\theta_{6}\]2 (A13) \[r_{5}\sin\theta_{5}+r_{4}\sin\theta_{4} =r_{1}\sin\theta_{1}+r_{6}\sin\theta_{6}\]3 (A14)and \(K_{1},K_{2},K_{3}\) by:  
\[r_{5}\sin\theta_{5}+r_{4}\sin\theta_{4} =r_{1}\sin\theta_{1}+r_{6}\sin\theta_{6}\]4 \[r_{5}\sin\theta_{5}+r_{4}\sin\theta_{4} =r_{1}\sin\theta_{1}+r_{6}\sin\theta_{6}\]5 (116) \[r_{5}\sin\theta_{5}+r_{4}\sin\theta_{4} =r_{1}\sin\theta_{1}+r_{6}\sin\theta_{6}\]6  
Having obtained \(\theta_{6}\) with Equation (6), \(\theta_{2}\) can be solved. Then also \(\theta_{4}\) is found by using Equation (118). \[r_{5}\sin\theta_{5}+r_{4}\sin\theta_{4} =r_{1}\sin\theta_{1}+r_{6}\sin\theta_{6}\]7  
Then the equation solving for \(\theta_{8}\) is shown in (119).