Systematic Sensitivity Analysis of Spatial One-DOF Models of Diarthrodial Joints

The identification of an equivalent mechanism which may reproduce at best the relative passive motion of the main anatomical structures of a human articulation is a target of great importance in the study of diarthrodial joints. Passive motion, that is the motion of the joint under virtually unloaded condition, is of basic importance for understanding the role of elements like bones, ligaments, etc. The identification is based on measurements performed during in vitro experiments. Passive motion of a number of human diarthrodial joints may be reproduced by equivalent mechanisms. However, the most critical points when devising the equivalent mechanism are represented by the changes of the subject articulation geometry due to age, sex, body constitution, etc. Thus, the equivalent mechanism sensitivity to the variations of the geometric parameters needs a careful investigation. The passive motion of many diarthrodial joints can be modeled by an equivalent mechanism with one degree of freedom (dof). This paper shows how the sensitivity of a one-dof equivalent mechanism with a finite number of geometric parameters can be studied in a systematic way. A sensitivity index together with some coefficients, called influence coefficients, are proposed which enable measuring the sensitivity of a mechanism, thus allowing the comparison of different equivalent mechanisms from the sensitivity viewpoint. Finally, a case study shows the application of the proposed methodology.