Types of Parallel Mechanisms
Based on the number of loop, a parallel mechanism can be either single-loop or multi-loop. Based on the dimension, a parallel mechanism can be either planar or spatial. Based on the symmetry of the limb topology, a parallel mechanism can be either symmetric or non-symmetric.
Another common classification of parallel mechanisms is based on the number and types of the end-effector DOF. Based on the number of end-effector DOF, they can be broadly classified into: 1) full-mobility parallel mechanisms, i.e. 6-DOF parallel mechanisms, and 2) lower-mobility parallel mechanisms, i.e. parallel mechanisms having less than 6 DOFs. Based on the types of its end-effector freedom, a parallel mechanism can be either translational, rotational/spherical, or mixed.
Parallel mechanisms can also be classified into fully-parallel and partially-parallel mechanisms. A fully-parallel mechanism is a parallel mechanism in which the number of limbs is equal to the number of DOF, and each limb has only one actuator. Otherwise, it is partially-parallel.
Parallel mechanism can also be classified into overconstrained and non-overconstrained mechanisms. A parallel mechanism is overconstrained if it has a full cycle mobility although it does not satisfy the Chebychev-Grübler-Kutzbach (CGK) mobility criterion. In other words, an overconstrained mechanism has a mobility although it should be a structure according to the CGK formula. An overconstrained mechanism would result in lower cost corresponding to the lower number of DOF, which would mean less number of joints. It also can increase the stiffness of the mechanism.
With regard to the motion coupling, parallel mechanism can be: 1) fully coupled, 2) decoupled, 3) half-decoupled, or 3) uncoupled. This can be known by observing the Jacobian matrix of the mechanism. However, based on how the Jacobian matrix looks like, we can add two more types of parallel mechanism: 1) maximally regular and 2) fully-isotropic.
We know that a Jacobian matrix has elements corresponding with the task space DOFs. We also know that a Jacobian matrix maps the velocity of the joint space to that of the task space.
The Jacobian matrix of a maximally regular parallel mechanism is an identity matrix. This means that the velocity of its joint space is transferred equally to the task space. The Jacobian matrix of a fully-isotropic parallel mechanism is a diagonal matrix with identical diagonal elements throughout its workspace.
An uncoupled parallel mechanism has a diagonal Jacobian matrix with different diagonal elements. A half-decoupled parallel mechanism has a full Jacobian matrix but translations and rotations are decoupled. A decoupled parallel mechanism has a triangular Jacobian matrix. A coupled parallel mechanism has a full Jacobian matrix.