R. Di Gregorio

A Translational 3-dof Parallel Manipulator

This paper presents a new architecture of a three degree-of-freedom parallel manipulator that, if properly assembled, exhibits pure translational motion of the output link (platform) with respect to the frame (base). To prove the existence of a pure translational motion a mobility analysis of the manipulator has been carried out. Moreover, a singularity analysis has also been conducted that shows the occurrence of configurations of the manipulator where the pure translational feature is no longer controllable.

Statics and singularity loci of the 3-UPU wrist

The static analysis of a parallel wrist, known as the 3-universal-prismatic-universal (UPU) wrist, is presented, and the 3-UPU wrist singularity conditions are interpreted from a statics point of view. An equation (singularity equation) that enables finding all the 3-UPU wrist singular configurations is written in explicit form. Moreover, the use of the Rodrigues parameters to parameterize the 3-UPU wrist platform orientation allows the singularity equation to become a fourth-degree polynomial equation in three unknowns. Finally, a numerical example is presented.

Mathematical models of passive motion at the human ankle joint by equivalent spatial parallel mechanisms.

The paper presents a theoretical model of the ankle joint, i.e. tibio-talar articulation, which shows how the articular surfaces and the ligaments, acting together as a mechanism, can control the passive kinematics of the joint. The authors had previously shown that, in virtually unloaded conditions, the ankle behaves as a single degree-of-freedom system, and that two ligament fibres remain nearly isometric throughout the flexion arc. Two different equivalent spatial parallel mechanisms together with corresponding kinematic models were formulated. These assumed isometricity of fibres within the calcaneal-fibular and tibio-calcaneal ligaments and rigidity of the articulating surfaces, taken as three sphere-plane contacts in one model, and as a single spherical pair in the other. Geometry parameters for the models were obtained from three specimens. Motion predictions compare quite well with the measured motion of the specimens. The differences are accounted for by the simplifications adopted to represent the complex anatomical structures, and might be reduced by future more realistic representations of the natural articular surfaces.

Parallel Mechanisms Applied to the Human Knee Passive Motion Simulation

This paper proposes a new mathematical solution of the forward kinematics of a one-degree of freedom mechanism for passive knee motion simulation that has been presented in the recent literature. The equivalent mechanism of the knee joint relies upon the assumption that fibers within the anterior cruciate ligament (ACL), the posterior cruciate ligament (PCL) and the medial collateral ligament (MCL) are isometric in passive relative motion of the femur and tibia condyles which, in turn, are modeled as spherical and planar surfaces respectively, with a single point of contact in the medial and lateral compartments. The paper also presents the mathematical model of a new mechanism that allows the modelling of spherical tibial condyles, thus overcoming the limitation of the previous mechanism. Finally, comparison with experimental results shows the benefits of the new mechanism.

Workspace and Optimal Design of a Pure Translation Parallel Manipulator

This paper presents a study of a pure translation three degrees of freedom fully-parallel manipulator, known as the Tsai manipulator. Based on the static analysis and on the determination of the singularity loci of the manipulator, criteria for the optimal geometric design of the manipulator for a given workspace free from singularities are proposed.

Kinematics of the 3-RSR wrist

Among the new architectures for parallel wrists, recently presented in the literature, one of the simplest is the architecture of the 3-revolute-spherical-revolute (RSR) wrist. The kinematics of the 3-RSR wrist has not been presented yet, in the literature. This paper presents the kinematic analysis of the 3-RSR wrist. In particular, the demonstration that the 3-RSR wrist makes the end-effector perform finite spherical motion is reconsidered from a different point of view. The new demonstration directly provides the constraint singularities of the 3-RSR wrist. Moreover, the position analysis of the 3-RSR wrist is reduced to the solution of problems already solved in the literature. Finally, the mobility analysis of the 3-RSR wrist is addressed, and all its singularity conditions are found in analytical form and geometrically interpreted.

DYNAMIC PERFORMANCE INDICES FOR 3-DOF PARALLEL MANIPULATORS

This paper presents three new indices for the characterization of the dynamic behavior of 3-dof parallel manipulators. The first index measures the dynamic isotropy of the manipulator, whereas the second and the third indices measure the manipulator swiftness, that is the manipulator capability to produce end-effector acceleration. They allow dynamic behavior of different manipulators to be compared. The indices can be easily expressed as functions of both the parameters locating the end-effector pose and the inertial and the geometric parameters of the links Moreover, based on their properties, a simple design procedure to size a three-dof manipulator so that it fulfills given dynamic requirements is presented.

Singularity Locus of 6–4 Fully-Parallel Manipulators

This paper presents a new analytic expression for the singularity locus of 6–4 fullyparallel manipulators (FPMs) with two double spherical pairs. The new expression allows the separation of the geometric constant parameters from the configuration dependent ones, and it is specially useful for designing manipulators referable to this architecture. The presented expression is deduced from a singularity-locus expression previously proposed by the author for the general Gough–Stewart platform, and it highlights that the shape of the singularity locus depends on the properties of a 3 × 3 matrix.

On the direct problem singularities of a class of 3-DOF parallel manipulators

The 3-PS structure features one rigid body (platform) connected to another rigid body (base) by means of three kinematic chains (limbs) of type PS (P and S stand for prismatic pair and spherical pair, respectively). All the 3-degree-of-freedom parallel manipulators with three connectivity-5 limbs, each one constituted of one passive (i.e. not actuated) prismatic pair, one passive spherical pair and one actuated kinematic pair of any type, become 3-PS structures when the actuated pairs are locked. Direct kinematics of this class of manipulators is tied to the properties of the 3-PS structure. In particular, the direct position analysis is tied to the assembly modes of the 3-PS structure; whereas the determination of the singularities of the direct instantaneous problem is tied to the determination of the singular geometries of the 3-PS structure, where instantaneous relative motions between platform and base are possible. The solution of these two problems is necessary both for designing the manipulators and for controlling them during motion. This paper deal with the determination of the singular geometries of the 3-PS structure.

Kinetostatics and Optimal Design of a 2PRPU Shoenflies-Motion Generator

Schoenflies-motion generators (SMGs) are 4-degrees-of-freedom (dof) manipulators whose end effector can perform translations along three independent directions and rotations around one fixed direction (Schoenflies motions). The authors, in a previous paper, showed that a 2PRPU SMG has a simple position analysis and singularities that leave a wide free-from-singularity workspace. The present paper addresses the kinetostatics and the optimal design of this SMG.