The lower-mobility parallel mechanism (PM) has fewer than six degrees of freedom (DoFs) and requires fewer links, joints and actuators than its 6-DoF counterpart. Hence, the use of the lower-mobility PM may save much cost in those applications requiring less mobility. In this paper, the type synthesis of symmetrical lower-mobility PMs is performed systematically using the constraint-synthesis method. First, some important theoretical fundamentals of type synthesis of lower-mobility PMs are investigated, including a classification of symmetry of lower-mobility PMs, the identification of instantaneous mechanisms and input selection method. Moreover, the difficult problem of how to correctly apply the general Grübler-Kutzbach criterion to lower-mobility PMs is solved. A mobility analysis of PMs with a closed loop in the limbs is also presented to demonstrate the validity. The type synthesis of 5-DoF and 4-DoF PMs is then dealt with in detail. Enumerations of novel 5-DoF and 4-DoF PMs are presented. The characteristics of constraint and structure of 5-DoF and 4-DoF PMs are also proposed. In addition, some novel 3-DoF PMs are presented.

This paper presents a new family of symmetrical lower-mobility parallel mechanisms (PMs) with spherical and parallel subchains, which consists of two 5-DOF (degrees of freedom) PMs, one 4-DOF PM and five 3-DOF PMs. The basic feature of this family is that each limb consists of five revolute pairs and can be constructed with two subchains, a 2R pointing subchain and a 3R parallel subchain, or a 3R spherical subchain and a 2R parallel subchain. Different geometrical arrangements of the limbs lead to different degrees of freedom. All the PMs of this family can be modularized easily due to the simple structure of the subchains.

Mobility analysis of a novel 3-5R parallel mechanism family whose limb consists of a 2R and a 3R parallel subchain is performed by the aid of screw theory. A mobility criterion applicable to such 3-leg parallel mechanisms in which each kinematic chain contains five kinematic pairs is proposed. It is shown that under different structural conditions, the 3-5R parallel mechanism can have 3, 4, or 5 DOF (degrees of freedom). The structural conditions that guarantee the full-cycle mobility are analyzed. The analysis and the method presented in this paper will be helpful in using such a 3-5R parallel mechanism family and introduce new insights into the mobility analysis of parallel mechanisms.

The assembly condition of universal pairs in the 3-UPU parallel mechanism determines the mechanism mobility. This paper uses reciprocal screw theory to study mobility analysis of the 3-UPU parallel mechanism under several different assembly conditions. The analysis and the method presented in this paper will be helpful in using the 3-UPU parallel mechanism and introduce new insights into the mobility analysis of parallel mechanisms.

This paper gives a brief description of some novel lower-mobility parallel mechanisms developed in our recent research, including two 4-DOF (degrees-of-freedom) parallel mechanisms and two 5-DOF parallel mechanisms. The two 4-DOF parallel mechanisms can perform three dimensional rotations and one translation. The two 5-DOF parallel mechanism can perform three dimensional rotations and two translations. All of these novel parallel mechanisms have symmetrical mechanical structures.