This book formulates the large deformation of a 3-D compliant beam as a boundary value problem (BVP). Unlike other methods, such as finite element (FE) method, that formulate problems based on displacements and/or rotational angles, the BVP formulation has been derived using curvatures that are more fundamental in presenting nonlinear geometries. Since in the case of finite rotation, superposition holds for curvatures but not for rotational angles, the model is much simpler and the resulting computational process is more efficient. The above advantages have been employed in this research to analyze compliant mechanism designs using curvature-based beam models. Along with the method of deriving the compliant members in the same global reference frame, a generalized constraint acting on a compliant mechanism is presented to replace traditional boundary constraints (such as fixed, pinned or sliding constraint) where none or only one degree of freedom (DOF) is allowed. Inspired by the dexterity of a natural biological joint that offers efficient multi-axis rotation, this research extends to the modeling method of a generalized constraint (or referred to here as a bio-joint constraint) to develop designs emulating commonly observed human motions of multi-DOFs . Using a multiple shooting method (MSM), the BVP is treated as an initial value problem and higher order accuracy can be achieved than finite element (FE) methods.
