Foto del docente

Marco Carricato

Associate Professor

Department of Industrial Engineering

Academic discipline: ING-IND/13 Applied Mechanics

Coordinator of PhD Programme of Mechanics and Advanced Engineering Sciences

Research

  • Synthesis of parallel manipulators
  • Singular configurations of mechanisms
  • Dynamics of spatial manipulators
  • Balancing of spatial manipulators
  • Theory of screws
  • Homokinetic transmissions
  • Cable-driven parallel manipulators
  • Compliant mechanisms


MAIN FIELDS OF RESEARCH

Dr. Marco Carricato has performed his scientific research in the following fields:

  1. Compliant mechanisms
  2. Synthesis of parallel robotic manipulators
  3. Singular configurations of mechanisms
  4. Dynamics of spatial manipulators
  5. Balancing of spatial manipulators
  6. Theory of screws
  7. Cable-driven parallel robots

Each topic is briefly presented hereafter and the main accomplishments emphasized. Publications are cited referring to the indexed list provided in the end.

A. Compliant mechanisms

This research was developed at the Center for Intelligent Machines and Robotics of the University of Florida (Gainesville, USA), mainly in collaboration with the late Prof. Joseph Duffy.

Compliant mechanisms achieve some or all of their motion and force transmission capabilities by virtue of the elastic deformation of some of their components. They have been successfully employed in a number of robotic applications dedicated to both macro and micro manipulation, in order to improve kinetostatic and control performances as well as mechanical design.

The research in this field focuses on two issues. The first one concerns the study of the properties of the stiffness matrix, which maps an incremental change in the forces applied to a mechanism to the corresponding variation of its equilibrium configuration [NP.3]. It is shown that such a map is not necessarily symmetric, depending on the presence of non-conservative terms in the mechanism energetic balance, as well as on the specific choice of the generalized coordinates describing the system configuration. The mathematical relationship with the Hessian matrix of the total potential energy is investigated in the case of conservative systems.

The second issue is related to the identification of safe working areas, in which compliant mechanisms may operate in conditions of guaranteed stability. The problem is dealt with by catastrophe theory, a powerful tool for the analysis of the topology of the equilibrium configurations. The stability analysis of a planar mechanism with flexural pivots is carried out as an application example {[IJ.12], [NP.2]}. For this mechanism, the inverse static analysis, consisting in detecting the entire set of equilibrium configurations corresponding to an assigned ensemble of external loads, is also performed {[IJ.13], [IC.14]}.

B. Synthesis of parallel robotic manipulators

A relevant part of this research was developed in collaboration with Prof. Vincenzo Parenti Castelli, from the University of Bologna, Italy.

In order to overcome the typical drawbacks of closed-chain mechanisms (e.g. limited dexterity, involved kinematic relations, critical singularities) while preserving their favorable characteristics (e.g. large payload to robot weight ratio, stiffness, high dynamic performances), innovative families of parallel manipulators are conceived, for translational {[IJ.8]-[IJ.11], [IC.7]-[IC.11], [P.2]}, Schoenflies [IJ.6] and rotational motion {[IJ.2], [IJ.7], [IC.6], [IC.12], [IC.13], [P.1]}. Such mechanisms prove valuable in the fields of automated assembly and machine tools as alternatives to serial positioning and orienting systems. In many cases, the proposed architectures exhibit decoupled output motion, i.e. each base-mounted motor directly actuates one of the output degrees of freedom (dofs), so that the kinematic analysis is simplified and the computation speed for real-time control is improved {[IJ.2], [IJ.6], [IJ.7], [IJ.11], [IC.6], [IC.9], [IC.12], [IC.13], [P.1]}. Several of these mechanisms also exhibit constant and one-to-one input-output kinetostatic relations, so that the behavior in terms of force and velocity transmission is maximally regular throughout the workspace and singularities are potentially ruled out {[IJ.2], [IJ.6], [IJ.11], [IC.6], [IC.9], [P.1]}.

As far as rotational mechanisms are concerned, it is worth emphasizing that there are insurmountable theoretical reasons that preclude the possibility of obtaining constant one-to-one relationships between the actuator velocities and the components of the angular velocity of the end-effector, when this may rotate about more than one direction and only holonomic joints are used. Closed-chain manipulators actuated by base-mounted motors may be designed, however, that exhibit direct Jacobian matrices constantly equal to the identity. Such architectures rule out the most troublesome singularities affecting closed-chain mechanisms and meaningfully regularize the transmission of forces and velocities throughout the workspace {[IJ.2], [IC.6], [P.1]}.

C. Singular configurations of mechanisms

Singular phenomena limit or prevent the correct operation of mechanisms. The research in this area focuses on two issues.

The first one, developed in collaboration with the PhD student M. Conconi {[IJ.3], [BC.3]}, concerns the taxonomy of singularities. Singularities are traditionally studied and classified from the viewpoint of the effects that they produce on ‘ready-to-use' mechanisms, characterized by a given frame, output member, actuated joints, etc. Such an approach may conceal the physical causes of singularities, making their interpretation unnecessarily complex and/or ambiguous. This research aims at providing an exhaustive taxonomy (i) recognizing hierarchical levels in which the physical causes of different phenomena may be distinguished and more easily interpreted, (ii) employing analytical tools making the physical comprehension of singularities particularly easy.

The second topic deals with the problem of singularities in homokinetic-transmission-based mechanisms [IJ.2]. The key point consists in that a mechanism that exhibit constant input-output relationships is not a priori singularity-free. Indeed, input-output homokinesis does not necessarily entail uniformity in the global kinetostatic behavior. While the forces and velocities produced by the actuators may be available on the end-effector unscaled and undistorted throughout the workspace, the same may not be said in general for the forces and velocities transmitted within the mechanism, which may remarkably vary during the movement and even rise to unacceptable values. In this perspective, the most common homokinetic transmissions are analyzed, with particular attention being dedicated to homokinetic couplings for intersecting shafts. Such transmissions, commonly used in automotive and industrial driveshafts, are proposed in {[IJ.2], [IC.6], [P.1]} for the design of innovative closed-chain rotational manipulators.

D. Dynamics of spatial manipulators

Such a research was developed at the Robotics Laboratory of the Laval University (Québec, Canada), in collaboration with Prof. Clément Gosselin.

The dynamic model of the Gough/Stewart Platform is investigated. This robot is a parallel manipulator whose mobile platform is connected to the fixed base by means of six extensible legs, each one of which is coupled at its extremities to a universal and a spherical joint. The study focuses on some issues, concerning the proper modeling of leg constraints, which seem to have been overlooked in a non-negligible part of the available literature related to the subject. It is shown, in particular, that the incorrect modeling of the constraints imposed by the universal joints may cause appreciable errors in the kinematic and dynamic analysis of the manipulator, thus originating inaccurate evaluations of the inertia forces. The effects of these errors are investigated and assessed for relevant cases of leg geometries, by performing numerical simulations aiming at identifying physically-consistent approximate models, that guarantee both improved computation quickness and adequate precision [IJ.5].

E. Balancing of spatial manipulators

Such a research was developed at the Robotics Laboratory of the Laval University (Québec, Canada), in collaboration with Prof. Clément Gosselin.

Static balancing of spatial parallel manipulators is a relatively recent topic of investigation. A mechanism is said to be statically balanced if zero external actions are required to maintain it at rest in any assumable configuration. Perfect balancing, by either counterweights or elastic elements, is accomplished, in the available literature, only for parallel manipulators in which the weight of the moving platform is sustained by legs comprising purely rotational joints. Indeed, balancing of parallel mechanisms with translational actuators, which are among the most common ones, is traditionally thought possible only by resorting to additional legs containing no prismatic pairs.

This research provides the conceptual and mechanical design of a balanced Gough/Stewart-type manipulator, in which the weight of the platform is entirely sustained by the legs comprising the extensible jacks, with no additional limbs being introduced. By the integrated action of elastic elements and counterweights, each leg is statically balanced and it generates, at its tip, a constant force contributing to maintaining the end-effector in neutral equilibrium. The feasibility of the proposed design is proven by numerically simulating both the static and the dynamic performances of a study prototype {[IJ.4], [IC.5]}.

In this field, experimental elastodynamic analyses have been also performed in order to provide more practical assessments of the reputed advantages brought-about by balancing on closed-chain mechanisms {[IC.4], [NP.1]}.

F. Theory of screws

Such a research was partially developed at the Department of Mechanical Engineering of the University of Guanajuato (Salamanca, México), in collaboration with Prof. José María Rico Martínez.

The exhaustive investigation of the vector subspaces of screws is of fundamental importance for the kinematic and static analysis of serial and parallel robots. It is known that there exist invariant screw subspaces (ISSs) that are subalgebras of the Lie algebra of the Euclidean group SE(3) and are in one-to-one correspondence with the subgroups of SE(3). An ISS is symmetric under arbitrary finite motions taking place about any screw belonging to the space itself. This property endows any ISS with remarkable characteristics. For instance, mechanical generators of an ISS (such as, for example, planar and spherical mechanisms) may be conveniently assembled by choosing more or less at random from ‘kits' of joints meeting some broad geometrical criteria (e.g. parallelism of axes, equality of pitches, etc.).

This research has the objective of identifying screw subspaces, addressed as persistent, that are more general than ISSs, though possessing most of their fundamental properties, such as: the ability to generate specific mechanisms by choosing joints according to broad specifications; the agreement with topological Grübler-like mobility criteria; the capability of generating reciprocal constraint spaces that remain congruent to themselves under finite rigid motions (such a property has special importance in the design of parallel mechanisms with specific output-motion characteristics). The exhaustive unfoldment and classification of persistent screw subspaces of dimension 2, 3 and 4 is carried out in {[BC.2], [IC.1]}.

G. Cable-driven parallel robots

Such a research was partially developed at the French National Institute for Research in Computer Science and Control - INRIA (Sophia Antipolis, France), in collaboration with Dr. Jean-Pierre Merlet.

Cable-driven parallel robots (CDPRs) employ cables in place of rigid-body extensible legs in order to control the posture of the end-effector, thus strengthening classic advantages characterizing closed-chain architectures while providing peculiar advantages (such as a larger workspace, reduced manufacturing and maintenance costs, ease of assembly and disassembly, etc.). A CDPR is defined as under-constrained if the end-effector preserves some mobility once actuators are locked and, thus, cable lengths are fixed. Typically, this occurs when the end-effector is controlled by a number of cables n smaller than the number of degrees of freedom that the end-effector possesses with respect to the base. A major challenge in the study of these robots consists in the intrinsic coupling between kinematics and statics (or dynamics), since the end-effector posture depends on both the actuator inputs and the applied forces. This coupling makes the position problems, which are aimed at determining the overall robot configuration when a set of n variables is assigned, especially difficult.

A general methodology is proposed in {[IJ.1], [BC.1]} for the kinematic, static and stability analysis of general under-constrained CDPRs. An original geometrico-static model is conceived, effective elimination procedures (based on Groebner bases, Sylvester's dialytic method, homotopy continuation, etc.) that allow position problems to be solved are presented and equilibrium stability is efficiently assessed within the framework of a constrained optimization problem. General under-constrained robots with by 2 and 3 cables are successfully solved as application examples {[IJ.1], [IC.2], [IC.3]}.


Bibliografia / References

International Journal Papers

[IJ.1]         Carricato, M., and Merlet, J.-P. 2011. Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots: a General Theory. IEEE Transactions on Robotics, submitted.

[IJ.2]         Carricato, M. 2009. Decoupled and Homokinetic Transmission of Rotational Motion via Constant-Velocity Joints in Closed-Chain Orientational Manipulators. ASME Journal of Mechanisms and Robotics, 1(4), Paper No. 041008, pp. 1-14.

[IJ.3]         Conconi, M., and Carricato, M. 2009. A New Assessment of Singularities of Parallel Kinematic Chains. IEEE Transactions on Robotics, 25(4), pp. 757-770.

[IJ.4]         Carricato, M., and Gosselin, C. 2009. A Statically Balanced Gough/Stewart-type Platform: Conception, Design and Simulation. ASME Journal of Mechanisms and Robotics, 1(3), Paper No. 031005, pp. 1-16.

[IJ.5]         Carricato, M., and Gosselin, C. 2009. On the Modeling of Leg Constraints in the Dynamic Analysis of Gough/Stewart-Type Platforms. ASME Journal of Computational and Nonlinear Dynamics, 4(1), Paper No. 011008, pp. 1-8.

[IJ.6]         Carricato, M. 2005. Fully Isotropic Four-Degrees-of-Freedom Parallel Mechanisms for Schoenflies Motion. Int. Journal of Robotics Research, 24(5), pp. 397-414.

[IJ.7]         Carricato, M., and Parenti-Castelli, V. 2004. A Novel Fully Decoupled Two-Degrees-of-Freedom Parallel Wrist. Int. Journal of Robotics Research, 23(6), pp. 661-667.

[IJ.8]         Carricato, M., and Parenti-Castelli, V. 2003. A Family of 3-DOF Translational Parallel Manipulators. ASME Journal of Mechanical Design, 125(2), pp. 302-307.

[IJ.9]         Carricato, M., and Parenti-Castelli, V. 2003. Position Analysis of a New Family of 3-DOF Translational Parallel Manipulators. ASME Journal of Mechanical Design, 125(2), pp. 316-322.

[IJ.10]     Carricato, M., and Parenti-Castelli, V. 2003. Kinematics of a Family of Translational Parallel Mechanisms with Three 4-DOF Legs and Rotary Actuators. Journal of Robotic Systems, 20(7), pp. 373-389.

[IJ.11]     Carricato, M., and Parenti-Castelli, V. 2002. Singularity-Free Fully-Isotropic Translational Parallel Mechanisms. Int. Journal of Robotics Research, 21(2), pp. 161-174.

[IJ.12]     Carricato, M., Duffy, J., and Parenti-Castelli, V. 2002. Catastrophe Analysis of a Planar System with Flexural Pivots. Mechanism and Machine Theory, 37(7), pp. 693-716.

[IJ.13]     Carricato, M., Parenti-Castelli, V., and Duffy, J. 2001. Inverse Static Analysis of a Planar System with Flexural Pivots. ASME Journal of Mechanical Design, 123(1), pp. 43-50.

Book Chapters

[BC.1]     Carricato, M., and Merlet, J.-P. 2010. Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots. In Advances in Robot Kinematics: Motion in Man and Machine, eds. J. Lenarčič and M.M. Stanišić, Springer, Dordrecht, pp. 309-319.

[BC.2]     Carricato, M., and Rico Martínez, J.M. 2010. Persistent Screw Systems. In Advances in Robot Kinematics: Motion in Man and Machine, eds. J. Lenarčič and M.M. Stanišić, Springer, Dordrecht, pp. 185-194.

[BC.3]     Conconi, M., and Carricato, M. 2008. A New Assessment of Singularities of Parallel Kinematic Chains. In Advances in Robot Kinematics: Analysis and Design, eds. J. Lenarčič and P. Wenger, Springer, Dordrecht, pp. 3-12.

International Conference Papers

[IC.1]       Carricato, M., and Rico Martínez, J.M. 2011. Persistent Screw Systems of Dimension Three. 13th World Congress in Mechanism and Machine Science, Guanajuato, Mèxico.

[IC.2]       Carricato, M., and Merlet, J.-P. 2011. Inverse Geometrico-Static Problem of Under-Constrained Cable-Driven Parallel Robots with Three Cables. 13th World Congress in Mechanism and Machine Science, Guanajuato, Mèxico.

[IC.3]       Carricato, M., and Merlet, J.-P. 2011. Direct Geometrico-Static Problem of Under-Constrained Cable-Driven Parallel Robots with Three Cables. 2011 IEEE Int. Conference on Robotics and Automation, Shanghai, China.

[IC.4]       Martini A., Troncossi M., Carricato M., and Rivola A. 2009. Modal and Kineto-Elastodynamic Analyses of Balanced Four-Bar Linkages. Multibody Dynamics 2009, ECCOMAS Thematic Conference, Warsaw, Poland, pp. 1-20.

[IC.5]       Carricato, M., and Gosselin, C. 2008. A Statically Balanced Gough/Stewart-Type Platform. 2008 ASME Int. Design Engineering Technical Conferences, New York, NY, USA, Paper No. DETC2008-50000, pp. 1-11.

[IC.6]       Carricato, M. 2007. Homokinetic transmission of rotational motion via constant-velocity joints in closed-chain wrists. 12th World Congress in Mechanism and Machine Science, Besançon, France, pp. 284-290.

[IC.7]       Carricato, M., and Parenti-Castelli, V. 2004. On the Topological and Geometrical Synthesis and Classification of Translational Parallel Mechanisms. 11th World Congress in Mechanism and Machine Science, Tianjin, China, pp. 1624-1628.

[IC.8]       Carricato, M., and Parenti-Castelli, V. 2002. Comparative Position, Workspace and Singularity Analyses of Two Isotropic Translational Parallel Manipulators with Three 4-dof Legs. MuSMe 2002, Int. Symposium on Multibody Systems and Mechatronics, Mexico City, Mexico, Paper No. M22, pp. 1-15.

[IC.9]       Carricato, M., and Parenti-Castelli, V. 2002. Singularity-Free Fully-Isotropic Translational Parallel Manipulators. 2002 ASME Design Engineering Technical Conferences, Montreal, QC, Canada, Paper No. MECH-34323, pp. 1-10.

[IC.10]   Carricato, M., and Parenti-Castelli, V. 2001. A Family of 3-DOF Translational Parallel Manipulators. 2001 ASME Design Engineering Technical Conferences, Pittsburgh, PA, USA, Paper No. DAC-21035, pp. 1-8.

[IC.11]   Carricato, M., and Parenti-Castelli, V. 2001. Position Analysis of a New Family of 3-DOF Translational Parallel Manipulators. 2001 ASME Design Engineering Technical Conferences, Pittsburgh, PA, USA, Paper No. DAC-21036, pp. 1-10.

[IC.12]   Carricato, M., and Parenti-Castelli, V. 2001. A 2-DOF Parallel Mechanism for a Human Shoulder Prosthesis. RAAD 2001, 10th Int. Workshop on Robotics in Alpe-Adria-Danube Region, Vienna, Austria, Paper No. RD-093, pp. 1-6.

[IC.13]   Carricato, M., and Parenti-Castelli, V. 2001. A Two-Decoupled-DOF Spherical Parallel Mechanism for Replication of Human Joints. Servicerob 2001, European Workshop on Service and Humanoid Robots, Santorini, Greece, pp. 5-12.

[IC.14]   Carricato, M., Parenti-Castelli, V., and Duffy, J. 2000. Inverse Static Analysis of a Planar System with Spiral Springs. 2000 ASME Design Engineering Technical Conferences, Baltimore, MD, USA, Paper No. MECH-14199, pp. 1-10.

National Papers

[NP.1]      Martini A., Troncossi M., Carricato M., and Rivola A. 2008. On the Elastodynamic Behaviour of Balanced Closed-Loop Mechanisms: Numerical Analysis of a Four-Bar Linkage. 2nd Workshop in Honour of Ettore Funaioli, eds. U. Meneghetti, A. Maggiore, V. Parenti-Castelli, Asterisco Edizioni, Bologna, pp. 1-12.

[NP.2]      Carricato, M., Duffy, J., and Parenti-Castelli, V. 2000. Catastrophe Analysis of a Planar System with two Spiral Springs. Pubbl. No. 112, DIEM − University of Bologna, pp. 1-28.

[NP.3]      Carricato, M., Duffy, J., and Parenti-Castelli, V. 2000. The Stiffness Matrix and the Hessian Matrix of the Total Potential Energy in Mechanisms. Pubbl. No. 111, DIEM − University of Bologna, pp. 1-17.

Patents

[P.1]          Carricato, M., and Conconi, M. 2010. Closed-Chain Rotational Mechanism Having Decoupled and Homokinetic Actuation. International (WIPO) Patent No. WO2010/134119 (A1).

[P.2]          Carricato, M., and Parenti-Castelli, V. 2005. Meccanismo Parallelo a Tre Gradi Di Libertà con Piattaforma Traslante (3-DOF Parallel Mechanism with Translating Platform). Italian Patent No. 0001326349.