Parallel mechanism (PM) with limbs of embedding structures means that the limbs in the mechanism are connected in the coupling structure, so as to realize limb coupling, and the PM of common axes between limbs. Characterized by the compact structure, low cost and larger workspace, this kind of PM has very broad application prospects in engineering. In this paper, analysis and improvement are carried out on the input of a compact 3-DOF PM with limbs of embedding structures with larger workspace.

The Beam Constraint Model (BCM) may yield large predicting errors (> 5 %) when the applied axial force goes beyond a certain boundary. We mathematically determine the nondimensional boundary of the axial force by the conditions of the positive definite quadratic form of the strain energy expression and the buckling load expressions. If the axial force is beyond the boundary, the Chained Beam Constraint Model (CBCM) can be used instead.

An alternative design method of the double-layer combined die using autofrettage theory is proposed. The relationship between the autofrettage pressure and the yield radius of the die insert is obtained, and expressions of residual stresses and displacements, which are directly related to geometric parameters, material properties and internal pressure, are derived. Compared with the conventional combined die, the autofrettaged die can bear larger working pressure, as expected.