Parallel manipulators (PMs) with decoupled kinematics can be obtained by combining a translational PM (TPM) with a spherical PM (SPM) either in multiplatform architectures or in integrated more-complex architectures. Some of the latter type are inspired by the 6–4 fully parallel manipulator (6–4 FPM), whereas others of the same type are deduced by suitably combining TPMs' limbs and SPMs' limbs into more cumbersome limbs which contain more than one actuated joint. The decoupled PMs (DPMs) presented here pursue an intermediate concept between the last two which keeps all the actuators on or near to the base in a simplified architecture with only three limbs. These features preserve the lightness of the mobile masses, together with the associated good-dynamic performances, and reduce the limitations on the workspace due to the eliminated limbs and to possible limb interferences. The finite and instantaneous kinematics of the proposed DPMs is studied, thus proving the practical implementation of the proposal.

In parallel mechanisms, singular configurations (singularities) have to be avoided during motion. All the singularities should be located in order to avoid them. Hence, relationships involving all the singular platform poses (singularity locus) and the mechanism geometric parameters are useful in the design of parallel mechanisms. This paper presents a new expression of the singularity condition of the most general mechanism (6-6 FPM) of a class of parallel mechanisms usually named fully-parallel mechanisms (FPM). The presented expression uses the mixed products of vectors that are easy to be identified on the mechanism. This approach will permit some singularities to be geometrically found. A procedure, based on this new expression, is provided to transform the singularity condition into a ninth-degree polynomial equation whose unknowns are the platform pose parameters. This singularity polynomial equation is cubic in the platform position parameters and a sixth-degree one in the platform orientation parameters. Finally, how to derive the expression of the singularity condition of a specific FPM from the presented 6-6 FPM singularity condition will be shown along with an example.

When a parallel manipulator reaches a singular configuration (singularity), the end effect (platform) pose cannot be controlled any longer, and infinite active forces must be applied in the actuated joints to balance the loads exerted on the platform. Therefore, these singularities must be avoided during motion. The first step to avoid them is to locate all the platform poses (singularity locus) making the manipulator singular. Hence, the availability of a singularity locus equation, explicitly relating the manipulator geometric parameters to the singular platform poses, greatly facilitates the design process of the manipulator. The problem of determining the platform poses, that make the 6-3 fully-parallel manipulator (6-3 FPM) singular, will be addressed. A simple singularity condition will be written. This singularity condition consists in equating to zero the mixed product of three vectors, that are easy to be identified on the manipulator, and it is geometrically interpretable. The presented singularity condition will be transformed into an equation (singularity locus equation) explicitly containing the geometric parameters of the manipulator and the platform pose parameters making the 6-3 FPM singular. Eventually, the singularity locus equation will be reduced to a polynomial equation by using the Rodrigues parameters to parameterize the platform orientation. This polynomial equation is cubic in the platform position parameters and one of sixth degree in the Rodrigues parameters.