Marco Carricato

A Family of 3-DOF Translational Parallel Manipulators

This article addresses parallel manipulators with fewer than six degrees of freedom, whose use may prove valuable in those applications in which a higher mobility is uncalled for. In particular, a family of 3-dof manipulators containing only revolute joints or at the most revolute and prismatic ones is studied. Design and assembly conditions sufficient to provide the travelling platform with a pure translational motion are determined and two sub-families that fulfill the imposed constraint are found: one is already known in the literature, while the other is original. The new architecture does not exhibit rotation singularities, i.e., configurations in which the platform gains rotational degrees of freedom. A geometric interpretation of the translation singularities is provided.

A Novel Fully Decoupled Two-Degrees-of-Freedom Parallel Wrist:

In this paper we present a novel pointing parallel mechanism with fully decoupled degrees of freedom. The mechanism consists of two interconnected slider-crank linkages, each one of which independently actuates one of the Euler angles of the output link. Motors can be mounted on the frame. The parallel architecture provides the mechanism with compactness and robustness, while decoupling of motion guarantees a wide workspace, an easy mathematical treatment, and a simple control. Such a mechanism may be suitable for applications that require aiming bodies such as tools, telescopes, antennas, cameras, solar panels, human or humanoid artificial limbs, particularly if requisites on dimensions and stoutness on the one hand and mobility on the other are stringent.

Fully Isotropic Four-Degrees-of-Freedom Parallel Mechanisms for Schoenflies Motion

This paper presents a novel family of fully isotropic parallel mechanisms whose output link is provided with Schoenflies motion, i.e., it can freely translate in space and rotate about a fixed direction. A methodology is proposed that makes use of the theory of screws to synthesize desired forms for both the direct and the inverse Jacobian matrices. In particular, these are made diagonal and constant throughout the workspace. Motors are mounted one per leg and each one of them actuates one of the degrees of freedom of the output body through a constant one-to-one velocity relation. As a consequence, motors may apply, with equal ease, a twist or a wrench of any amplitude (within the motor operation range) to the end-effector around any screw congruous with the admitted motion, so that full isotropy is achieved. Kinematic analysis is trivial and no computation is required for real-time control. Furthermore, actuator motion ranges can be easily related to the theoretical workspace dimensions and the problem of link interference is potentially simplified.

Stability Analysis of Underconstrained Cable-Driven Parallel Robots

This paper studies cable-driven parallel robots with less than six cables, in crane configuration. A geometrico-static model is provided, and the stability of static equilibrium is assessed within the framework of a constrained optimization problem. The method relies on ordinary linear-algebra routines, and it may be very simply applied to the most general architectures. Several examples are provided, concerning robots with a number of cables that range from 2 to 4.

A New Assessment of Singularities of Parallel Kinematic Chains

This paper presents a novel assessment of singularities of general parallel kinematic chains. Hierarchical levels in which different critical phenomena originate are recognized. At each level, the causes of singular events are identified and interpreted, and on their basis, a comprehensive taxonomy is proposed. First, the unactuated kinematic chain is studied. The concepts of leg and passive-constraint singularities are described, and stationary and increased instantaneous mobility configurations are identified. Then, a set of motorized joints is chosen. The effects of first-level singularities on the actuated chain are investigated, and further phenomena are identified, such as redundancy singularities and active-constraint singularities. The notions of reaction and action spaces are originally discussed. The consequences on the ability of the actuated chain to effectively govern its local and global freedoms are analyzed, and the complex interactions between the various singular events are studied. The instantaneous redundancy of actuators, which occur when these work either against each other or against joint constraints, is also evaluated. Finally, when the input-output mechanism is considered, the events described at the previous stages are interpreted within the perspective of the machines desired use.

Direct geometrico-static problem of under-constrained cable-driven parallel robots with three cables

This paper studies under-constrained cable-driven parallel robots with three cables. A major challenge in the study of these manipulators is the intrinsic coupling between kinematics and statics, which must be tackled simultaneously. In this contribution, a general elimination procedure is provided that solves the direct geometrico-static problem, which consists in determining the platform posture and the cable tensions when the cable lengths are assigned. The problem is proven to have up to 156 complex solutions.

Position Analysis of a New Family of 3-DOF Translational Parallel Manipulators*

This article presents the position analysis of a new family of 3-limbed 3-dof parallel manipulators, whose output links exhibit a motion of pure translation with respect to the base. Each limb contains four passive revolute joints and an active prismatic pair, which can be mounted anywhere along the kinematic chain or replaced by a fifth revolute one. A univariate polynomial has been found that solves the direct position problem wherever the actuators are placed. The inverse analysis has been carried out in closed-form for all possible locations of the actuated joints. Finally, numerical examples are provided.

Singularity-Free Fully-Isotropic Translational Parallel Manipulators

Parallel mechanisms show desirable characteristics such as a large payload to robot weight ratio, considerable stiffness, low inertia and high dynamic performances. In particular, parallel manipulators with fewer than six degrees of freedom have recently attracted researchers’ attention, as their employ may prove valuable in those applications in which a higher mobility is uncalled-for. The attention of this dissertation is focused on translational parallel manipulators (TPMs), that is on parallel manipulators whose output link (platform) is provided with a pure translational motion with respect to the frame. The first part deals with the general problem of the topological synthesis and classification of TPMs, that is it identifies the architectures that TPM legs must possess for the platform to be able to freely translate in space without altering its orientation. The second part studies both constraint and direct singularities of TPMs. In particular, special families of fully-isotropic mechanisms are identified. Such manipulators exhibit outstanding properties, as they are free from singularities and show a constant orthogonal Jacobian matrix throughout their workspace. As a consequence, both the direct and the inverse position problems are linear and the kinematic analysis proves straightforward.

Direct Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots with 4 Cables

This paper studies the direct geometrico-static problem of under- constrained parallel robots suspended by \(4\) cables. The task consists in determining the end-effector pose and the cable tensions when the cable lengths are assigned. The problem is challenging, because kinematics and statics are coupled and they must be solved simultaneously. An effective elimination procedure is presented that provides the complete solution set, thus proving that, when all cables are in tension, 216 potential solutions exists in the complex field. A least-degree univariate polynomial free of spurious factors is obtained in the ideal governing the problem and solutions are numerically computed via both an eigenvalue formulation and homotopy continuation. Equilibrium configurations with slack cables are also considered.

Inverse Geometrico-Static Problem of Underconstrained Cable-Driven Parallel Robots With Three Cables

This paper studies under-constrained cable-driven parallel robots with three cables. A major challenge in the study of these manipulators is the intrin- sic coupling between kinematics and statics, which must be dealt with simultaneously. In this contribution, gen- eral elimination procedures are provided that solve the inverse geometrico-static problem with assigned orienta- tion or position. In the former case, the platform orienta- tion is given, whereas the platform position and the cable lengths and tensions must be computed. In the latter case, the platform position is known, whereas the platform ori- entation and the cable lengths and tensions must be cal- culated. These problems are proven to admit up to 1 and 24 real solutions, respectively.