Based on the terminal constraints system (TCS) and reciprocal screw theory, a novel method is presented to determine the isotropic configurations of limited degree-of-freedom (DOF) parallel manipulators. From the available physical meaning of isotropy, the criteria to determine the isotropic configurations can be transformed to investigate whether the TCS acting on the moving platform works equally well in all directions. From the TCS study, the simplest form of constraints system matrix can be obtained. Then the constraint condition number is defined to measure the isotropy of spatial parallel manipulator based on the TCS. This method not only avoids solving the Jacobian matrix for some complex structural parallel manipulators but also points out the physical meaning of isotropy, which indicates that the TCS acting on the moving platform works equally well in all directions. Three examples are employed to illustrate this method.

Singularities of a manipulator have been addressed repeatedly. However, the singularities and the degree(s) of freedom, as a matter of fact, are two different aspects of the mobility of a manipulator. Consequently, this paper dedicates to discussing the mobility properties through mobility space, which synchronously define the type, number and direction characteristics of the independent motions that the manipulator should execute. The mobility space of a manipulator can be obtained with reciprocal screws of the manipulator via singular value decomposition, which instantaneously depicts the singularity and mobility problems of the manipulators. Application example demonstrates that this methodology can investigate the all-sided mobility properties of parallel manipulators.