Carlo INNOCENTI - personale UniMoRe

Nuova ricerca

Carlo INNOCENTI

Professore Ordinario
Dipartimento di Ingegneria "Enzo Ferrari"

Pubblicazioni

2010 - Measurement over balls of conical involute gears [Relazione in Atti di Convegno]
Innocenti, C.
abstract

The paper reformulates the theory of the measurement over spheres of conical involute gears by simplifying its algebra and extending it to internal gears. Moreover, a five-measurement technique is proposed that retrieves information about all basic parameters of a conical involute gear. Numerical examples show application of the reported results to case studies. Copyright © 2009 by ASME.

2009 - Measurement over balls of conical involute gears [Relazione in Atti di Convegno]
Innocenti, C.
abstract

2008 - Designing Synchronous Belt Transmissions With Variable Velocity Ratio [Articolo su rivista]
Innocenti, Carlo; Paganelli, D.
abstract

The paper presents a new procedure to design a two-pulley synchronous belt transmission connecting, with no belt tensioner, two parallel-axis shafts with a variable velocity ratio. The procedure takes into account the limited number of choices for pitch and length of off-the-shelf synchronous belts, which translates into the need of fine-adjusting either the center distance or the law of motion. Differently from other approaches reported in the technical literature, the suggested method is based on the numerical solution of a set of functional equations. A numerical example shows application of the proposed method to a case study.

2008 - Harmonic balancing of planar machinery by arbitrarily placed counterweighing shafts [Relazione in Atti di Convegno]
Innocenti, C.
abstract

The paper proposes a new method to neutralize the shaking force and shaking moment exerted on its supporting structure by a one-degree-of-freedom machine whose non-stationary parts move parallel to the same plane. Differently from the well-known technique that takes advantage of two counterweighing shafts for each of the harmonic components of the frame excitation that has to be counteracted, the proposed method requires three shafts per harmonic component. This seemingly additional complexity is offset by the complete freedom of selection of the shaft axis positions, a feature not enjoyed by the classical two-shaft device. An example shows application of the proposed method to a four-cylinder in-line engine. Copyright © 2007 by ASME.

2008 - Optimal Choice of the Shaft Angle for Involute Gear Hobbing [Articolo su rivista]
Innocenti, Carlo
abstract

With reference to the machining of an involute spur or helical gear by the hobbing process, the paper suggests a new criterion for selecting the position of the hob axis relative to the gear axis. By adhering to the proposed criterion, the hob axis is set at the minimum distance from the gear axis, thus maximizing the depth of the tooth spaces of the gear. The new criterion is operatively implemented by solving a univariate equation, which stems from a new, synthetic analysis of the meshing of crossed-axis involute gears. A numerical example shows application of the suggested procedure to a case study and compares the optimal hob setting to the customary one.

2008 - The Kinematics of Conical Involute Gear Hobbing [Articolo su rivista]
Innocenti, Carlo
abstract

The paper is aimed at finding all relative rigid-body positions of two conical involute gears that mesh together with no backlash. The results are then specialized to determine two key setting parameters for a hobbing machine that has to cut a conical involute gear. A numerical example shows application of the presented results to a case study.

2007 - Optimal choice of the shaft angle for involute gear hobbing [Articolo su rivista]
Innocenti, C.
abstract

With reference to the machining of an involute spur or helical gear by the hobbing process, this paper suggests a new criterion for selecting the position of the hob axis relative to the gear axis. By adhering to the proposed criterion, the hob axis is set at the minimum distance from the gear axis, thus maximizing the depth of the tooth spaces of the gear. The new criterion is operatively implemented by solving a univariate equation, which stems from a new, synthetic analysis of the meshing of crossed-axis, involute gears. A numerical example shows application of the suggested procedure to a case study and compares the optimal hob setting to the customary one.

2007 - Statics as a means to assess the sensitivity of a manipulator to kinematic parameter deviations [Relazione in Atti di Convegno]
Innocenti, C.
abstract

The paper suggests a new method to determine the dependence of the pose of a manipulator end-effector on the dimensional variations of the manipulator rigid links. Based on the principle of virtual work, the method is applicable to all statically determinate manipulators, i.e., to the manipulators whose joint reactions can be found by resorting to equilibrium equations only. The distinctive feature of the proposed method over the previous ones is the ability to keep the complexity of the kinematic model of the analyzed manipulator to a minimum: no generalized kinematic model is necessary even in case a nominally special-geometry manipulator transforms into a general-geometry manipulator when geometric inaccuracies are taken into account. A numerical example shows application of the proposed method to a case study. Use of the method in kinematic calibration of manipulators is also outlined. © 2007 IEEE.

2007 - The kinematics of conical involute gear hobbing [Relazione in Atti di Convegno]
Innocenti, C.
abstract

2006 - Designing synchronous belt transmissions with variable velocity ratio [Relazione in Atti di Convegno]
Innocenti, C.; Paganelli, D.
abstract

2006 - Optimal choice of the shaft angle for involute gear hobbing [Relazione in Atti di Convegno]
Innocenti, C.
abstract

2006 - Position Analysis of the RRP-3(SS) Multi-Loop Spatial Structure [Articolo su rivista]
Innocenti, Carlo; P., Wenger
abstract

The paper presents the position analysis of a spatial structure composed of two platforms mutually connected by one RRP and three SS serial kinematic chains, where R, P, and S stand for revolute, prismatic, and spherical kinematic pair respectively. A set of three compatibility equations is laid down that, following algebraic elimination, results in a 28th-order univariate algebraic equation, which in turn provides the addressed problem with 28 solutions in the complex domain.Among the applications of the results presented in this paper is the solution to the forward kinematics of the Tricept, a well-known in-parallel-actuated spatial manipulator.Numerical examples show adoption of the proposed method in dealing with two case studies.

2005 - Positioning the base of spatial 2-dof regional manipulators in order to reach as many arbitrarily-chosen points in space as possible [Relazione in Atti di Convegno]
Innocenti, C.
abstract

Whenever a manipulator is assigned the repetitive task of moving a point of its end-effector through a limited number of prescribed positions in space, it might be possible to endow it with two degrees of freedom only - instead of the canonical minimum of three - on the condition that the base of the manipulator is suitably placed in space. This paper shows a procedure to determine the correct rigid-body position of the base of two-degree-of-freedom (2-dof) manipulators - either serial or fully-parallel - in order to enable them to accomplish the above-mentioned task. Numerical examples are reported. © 2005 IEEE.

2004 - Position analysis of the RRP-3(SS) multi-loop spatial structure [Relazione in Atti di Convegno]
Innocenti, C.; Wenger, P.
abstract

The paper presents the position analysis of a spatial structure composed of two platforms mutually connected by one RRP and three SS serial kinematic chains, where R, P, and S stand for revolute, prismatic, and spherical kinematic pair respectively. A set of three compatibility equations is laid down that, following algebraic elimination, results in a 28th-order univariate algebraic equation, which in turn provides the addressed problem with 28 solutions in the complex domain. Among the applications of the results presented in this paper is the solution to the forward kinematics of the Tricept, a well-known in-parallel-actuated spatial manipulator. Numerical examples show adoption of the proposed method in dealing with two case studies.

2002 - Kinematic clearance sensitivity analysis of spatial structures with revolute joints [Articolo su rivista]
Innocenti, Carlo
abstract

The paper presents a new method to assess the influence of joint clearances in spatial structures that are composed of links connected be revolute joints. The method allows assessment of the amount by which joint clearances affect the rigid-body position of a generic link of the structure when an external load is exerted on the link. Unlike other procedures, the proposed method relies on the clearance-free idealization of the structure under investigation. An example shows application of the proposed method to the analysis of the structure derived from a multi-loop manipulator by freezing its actuators.

2001 - Forward kinematics in polynomial form of the general Stewart platform [Articolo su rivista]
Innocenti, Carlo
abstract

The paper presents a new algorithm to solve, in polynomial form, the forward kinematics of the general-geometry 6-6 fully-parallel manipulator. The forty solutions that the problem at hand admits in the complex domain are found by determining the roots of a 40th-order univariate polynomial equation. Unlike the existing algorithm, the proposed one is suitable for implementation in a standard floating-point computation environment. A numerical example shows application of the new algorithm to a case study.

1999 - Kinematic clearance sensitivity analysis of spatial structures with revolute joints [Relazione in Atti di Convegno]
Innocenti, C.
abstract

The paper presents a new method to assess the influence of joint clearances in spatial structures that are composed of links connected by revolute joints. The method allows assessment of the amount by which joint clearances affect the rigid-body position of a generic link of the structure when an external load is exerted on the link. Unlike other procedures, the proposed method relies on the clearance-free idealization of the structure under investigation. An example shows application of the proposed method to the analysis of the structure derived from a multi-loop manipulator by freezing its actuators.

1998 - Closed-form determination of the location of a rigid body by seven in-parallel linear transducers [Articolo su rivista]
Innocenti, C.
abstract

The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study. © 1998 by ASME.

1998 - Forward kinematics in polynomial form of the general stewart platform [Relazione in Atti di Convegno]
Innocenti, C.
abstract

The paper presents a new algorithm to solve, in polynomial form, the forward kinematics of the generalgeometry 6-6 fully-parallel manipulator. The forty solutions that the problem at hand admits in the complex domain are found by determining the roots of a 40th-order univariate polynomial equation. Unlike the existing algorithm, the proposed one is suitable for implementation in a standard floating-point computation environment. A numerical example shows application of the new algorithm to a case study.

1998 - Singularity-free evolution from one configuration to another in serial and fully-parallel manipulators [Articolo su rivista]
Innocenti, C.; Parenti-Castelli, V.
abstract

Among the several ways adopted for the characterization of manipulator performances is identification of the typologies of maneuvers allowed by the manipulator kinematic arrangement. The multiplicity of configurations corresponding to a given hand position for serial manipulators, or to a given set of input values for fullyparallel manipulators, makes one wonder whether a manipulator can perform the maneuver of changing its configuration without meeting singularities. The paper shows that singularity-free configuration change is possible both for general-geometry serial and fully-parallel architectures. Results are reported that shed light on potential performances of manipulators and allow, in perspective, a deeper exploitation of their structural peculiarities. © 1998 by ASME.

1997 - Analysis of meshing of beveloid gears [Articolo su rivista]
Innocenti, C.
abstract

This paper analyses the meshing of a pair of beveloid gears mounted on intersecting or skew shafts. Precisely, the dependence of the backlash on the gear geometry and the shaft relative position are investigated. The study is preceded with the presentation of a new, basic nomenclature to describe the kinematically relevant dimensions of beveloid gears. Finally, a numerical example is reported. © 1997 Elsevier Science Ltd. All rights reserved.

1997 - Position analysis in analytical form of the 7-link assur kinematic chain featuring one ternary link connected to ternary links only [Articolo su rivista]
Innocenti, C.
abstract

The paper presents the analytical-form position analysis of one of the three existing 7-link Assur kinematic chains, precisely the one featuring three binary links and four ternary links, one of the ternary links being joined to the other three. The analysis results in a 14th order polynomial equation in one unknown whose 14 roots correspond, in the complex domain, to as many assembly configurations. The contribution widens the set of planar linkages whose kinematic analysis can be thoroughly and exhaustively solved. A case study is finally provided. © 1997 Elsevier Science Ltd. All rights reserved.

1996 - A framework for efficiency evaluation of multi-degree-of- freedom gear trains [Articolo su rivista]
Innocenti, C.
abstract

The paper proposes a new approach to the efficiency evaluation of any one- or multi-degree-of-freedom gear trains. The suggested approach generalizes the known procedures developed for two-degree-of-freedom gear trains. It is based on the determination of a vector whose components are the torques delivered to the shafts of the gear train. Furthermore the paper shows that, for a notable category of gear trains, such a vector can have only a finite number of directions, which implies that a limited number of experimental data suffices for estimating the efficiency at any operational condition. Examples of application of the proposed methodology are provided. © 1996 by ASME.

1996 - Closed-form determination of the location of a rigid body by seven in-parallel linear transducers [Relazione in Atti di Convegno]
Innocenti, C.
abstract

1995 - Analtical‐ form direct kinematicefor the second scheme of a 5–5 general‐geometry fully parallel manipulator [Articolo su rivista]
Innocenti, C.
abstract

This article presents the direct kinematics of a 6 degrees of freedom fully parallel manipulator that features five connection points on both base and platform. The considered leg arrangement is one of the two possible, the other having been referred to in a previous paper. The base and platform have a general geometry, i.e., the connection points are not bound to lie on planes. The direct kinematics is solved in analytical form, which allows determination of every possible solution. After a suitable set of five equations in five unknowns has been laid down, and an original elimination procedure applied, a final polynomial equation of the 24th order is found whose 24 solutions correspond to as many assembly configurations for the considered fully parallel manipulator. A case study is reported. © 1995 John Wiley & Sons, Inc. Copyright © 1995 Wiley Periodicals, Inc., A Wiley Company

1995 - Development of a new geneva mechanism with improved kinematic characteristics: Two station Geneva mechanisms [Articolo su rivista]
Innocenti, C.
abstract

1995 - Direct kinematics in analytical form of the 6-4 fully-parallel mechanism [Articolo su rivista]
Innocenti, C.
abstract

This paper presents the direct position analysis of the fully-parallel mechanism that features six connection points on the base and four on the platform. The shape of both base and platform is general and, in particular, not restricted to being planar. The analysis is performed first by writing a suitable set of five closure equations in five unknowns. Then, by a specifically-developed elimination scheme, the closure equation set is reduced to a 32nd-order algebraic equation with only one unknown, which proves free from extraneous roots. Hence 32 closure configurations of the 6-4 mechanism do exist in the complex field. A numerical example is reported that confirms the new theoretical results. © 1995 by ASME.

1995 - Polynomial solution of the spatial burmester problem [Articolo su rivista]
Innocenti, C.
abstract

This paper presents a new method for the dimensional synthesis of the spatial guidance linkage that features the guided body connected to the base by the interposition of five rods having spherical joints at both extremities. The linkage is required to index the guided body through seven arbitrarily-chosen rigid-body positions. Core of the proposed method is an original algebraic elimination procedure that allows five unknowns to be dropped from a set of six second-order algebraic equations in sbc unknowns. As a result, a final univariate polynomial equation of twentieth order is obtained whose twenty roots, in the complex domain, represent as many possible placements for a connecting rod. A numerical example is reported. © 1995 by ASME.

1995 - Polynomial solution to the position analysis of the 7-link assur kinematic chain with one quaternary link [Articolo su rivista]
Innocenti, C.
abstract

Following a couple of previous papers devoted to the position analysis of two different 7-link Assur kinematic chains, this paper presents the algebraic-form position analysis of the remaining 7-link Assur kinematic chain, which can be distinguished from the others because it alone features one quaternary link. The position analysis, devoted at determining all possible assembly configurations of the considered Assur kinematic chain, is performed by first devising a system of two algebraic equations in two unknowns. After dialytic elimination, a final polynomial equation of eighteenth order is found whose solutions provide, in the complex field, 18 assembly configurations for the examined Assur kinematic chain. As a corollary, it can also be stated that two coupler point curves drawn by two distinct four-bar linkages intersect each other at 18 real points at most. Finally, a numerical example shows application of the new theoretical results. © 1995.

1994 - Analytical-form position analysis of the 7-link assur kinematic chain with four serially-connected ternary links [Articolo su rivista]
Innocenti, C.
abstract

The paper addresses the position analysis of the 7-link Assur kinematic chain that features three binary links and four serially-connected ternary links. The analysis, aimed at finding all possible assembly configurations of the Assur kinematic chain, is carried out by first devising a set of three constraint equations in a corresponding number of unknowns. Then, by an original elimination procedure, two out of the three unknowns are simultaneously dropped out. As a result, a final algebraic equation of degree sixteen with only one unknown and free from extraneous roots is obtained. The sixteen solutions of this equation provide as many assembly configurations for the Assur kinematic chain in the complex field. Finally, a case study is reported. © 1994 by ASME.

1994 - Direct position analysis in analytical form of the parallel manipulator that features a planar platform supported at six points by six planes [Relazione in Atti di Convegno]
Innocenti, Carlo
abstract

The paper presents the direct position analysis of the parallel manipulator that features and end-effector with six coplanar spherical joints constrained to lie on x-y sliding tables. By properly controlling the postures of the sliding tables, the end-effector is endowed with up to six degrees of freedom with respect to the frame. The direct position analysis, aimed at determining all positions of the end-effector consistent with a given set of sliding table postures, is solved in analytical form by first devising a system of eight nonlinear compatibility equations in a corresponding number of unknowns. By an original elimination procedure, a final eighth-order univariate polynomial equation is obtained whose eight roots represent as many assembly configurations for the analyzed manipulator. A numerical example is finally reported which confirms the new theoretical results.

1994 - Exhaustive enumeration of fully parallel kinematic chains [Relazione in Atti di Convegno]
Innocenti, Carlo; Parenti-Castelli, Vincenzo
abstract

The direct position analysis of fully-parallel manipulators entails in essence the analysis of fully-parallel kinematic chains that feature two rigid bodies connected to each other via six binary links (legs) through spherical pairs. Some legs may share their endings, thus different leg arrangements are possible. The paper presents an original procedure for identification and exhaustive enumeration of fully-parallel kinematic chains. The enumeration leads to the identification of twenty-one different fully-parallel kinematic chains and provides the frame within which the state of the art in the field of direct position analysis of fully-parallel manipulators - or, more strictly, of fully-parallel kinematic chains - can be conveyed.

1994 - Managing discontinuity in dynamics [Relazione in Atti di Convegno]
Innocenti, Carlo
abstract

The paper proposes a method aimed at performing numerical integration of the equations of motion for dynamic systems whose behavior experiences discontinuity. The involved discontinuity can be both acceleration discontinuity and velocity discontinuity. The method is based on a timely detection of discontinuity occurrences and on updating the state matrix for selection of the suited set of motion equations.

1994 - Managing discontinuity in dynamics [Relazione in Atti di Convegno]
Innocenti, Carlo
abstract

The paper proposes a method aimed to performing numerical integration of the equations of motion for dynamic systems whose behavior experiences discontinuity. The involved discontinuity can be both acceleration discontinuity and velocity discontinuity. The method is based on a timely detection of discontinuity occurrences and on updating a state matrix for selection of the studied set of motion equations. Without loss of generality, the method is presented by referring to a single-degree-of-freedom system that undergoes Coulomb friction - static and kinetic - as well as instantaneous collisions. The reported results, obtained by a demonstrative PC program, show that both stick-slip phenomenon and characteristic impulsive dynamic behavior can be accurately predicted, even by reasonably large steps of integration, without numerical instability.

1994 - Polynomial solution of the spatial burmester problem [Relazione in Atti di Convegno]
Innocenti, Carlo
abstract

The paper presents a new method for the dimensional synthesis of the spatial guidance linkage that features the guided body connected to the base by the interposition of five rods having spherical joints at both extremities. The linkage is required to index the guided body through seven arbitrarily-chosen rigid-body positions. Core of the proposed method is an original algebraic elimination procedure that allows five unknowns to be dropped from a set of six second-order algebraic equations in six unknowns. As a result, a final univariate polynomial equation of twentieth order is obtained whose twenty roots, in the complex domain, represent as many possible placements for a connecting rod. A numerical example is reported.

1994 - Polynomial solution of the spatial burmester problem [Relazione in Atti di Convegno]
Innocenti, C.
abstract

The paper presents a new method for the dimensional synthesis of the spatial guidance linkage that features the guided body connected to the base by the interposition of five rods having spherical joints at both extremities. The linkage is required to index the guided body through seven arbitrarilychosen rigid-body positions. Core of the proposed method is an original algebraic elimination procedure that allows five unknowns to be dropped from a set of six second-order algebraic equations in six unknowns. As a result, a final univariate polynomial equation of twentieth order is obtained whose twenty roots, in the complex domain, represent as many possible placements for a connecting rod. A numerical example is reported.

1993 - Analytical form solution of the direct kinematics of a 4-4 fully in-parallel actuated six degree-of-freedom mechanism [Relazione in Atti di Convegno]
Innocenti, C.; Parenti-Castelli, V.
abstract

This paper presents the direct position analysis in analytical form of a six-degree-of-freedom 4-4 fully-parallel mechanism. For a given set of actuator displacements the mechanism becomes a structure and the analysis finds all the possible closures of the structure. The analysis is performed in two steps. First, the two closures of the tetrahedron-like subchain of the structure are found. Then, for each tetrahedron closure, two transcendental equations are determined that represent the closure of the remaining part of the 4-4 structure. The two equations can he reduced to algebraic equations and, after eliminating the unwanted unknowns, a final 8th order equation in only one unknown is obtained. Hence, the maximum number of possible real closures of the 4-4 structure is sixteen. Numerical examples are reported which illustrate and confirm the new theoretical result.

1993 - Closed-form direct position analysis of a 5-5 parallel mechanism [Articolo su rivista]
Innocenti, C.; Parenti-Castelli, V.
abstract

The paper presents the closed form direct displacement analysis for a class of Stewart platform-type parallel mechanisms whose general feature consists of six legs which meet five distinct points both in the base and in the movable output link. Out of the two possible arrangements, only one is here analyzed in detail. Given a set of actuator displacements the analysis provides all the possible locations of the platform relative to the base. The analysis results in a 40th degree polynomial equation in one unknown. The roots of the equation provide in the complex field forty closures of the mechanism. This new result has been numerically verified by the inverse displacement analysis. © 1993 by ASME.

1993 - Echelon form solution of direct kinematics for the general fully-parallel spherical wrist [Articolo su rivista]
Innocenti, C.; Parenti-Castelli, V.
abstract

This paper presents the echelon form direct position analysis of a class of fully in-parallel actuated mechanisms for the orientation of a rigid body with a fixed point. The mechanisms have a structure which is the most general one for manipulator spherical wrists with three degrees of freedom and fully-parallel arrangement. The analysis results in a two-equation system in echelon form; the first equation is of 8th order and the remaining is linear. As a consequence, when a set of actuator displacements is given, eight configurations of the mechanism are possible. A numerical example confirms the new theoretical result. © 1993.

1993 - Forward kinematics of the general 6-6 fully parallel mechanism: An exhaustive numerical approach via a mono-dimensional-search algorithm [Articolo su rivista]
Innocenti, C.; Parenti-Castelli, V.
abstract

A new numerical method for the solution of the direct position analysis of the six d.o.f. fully parallel mechanism with general geometry, often referred to as generalized Stewart platform mechanism, is presented. The main feature of the method, making it attractive with respect to the methods available in the literature, is the ability to find out all the real solutions of the direct position analysis. The effectiveness of the new algorithm relies upon the solution of only one equation in one unknown. That equation is strictly representative of the problem, i.e., it is free from extraneous roots and every solution of the direct position analysis entails the existence of a root for the equation. A case study is reported. © 1993 by ASME.

1992 - A new kinematic model for the closure equations of the generalized Stewart platform mechanism [Articolo su rivista]
Innocenti, C.; Parenti-Castelli, V.
abstract

The paper deals with the direct position analysis of the six degrees of freedom parallel manipulator known as generalized Stewart Platform Mechanism. When a set of actuator displacements is given the mechanism becomes a statically determined structure and the analysis solves for the closure of the structure. The governing equations are non-linear and many solutions are possible. Kinematic models reported in the literature relate to systems of six equations in six unknowns, which are solved numerically because of their complexity. Based on a novel approach, a new kinematic model of the structure is presented in this paper. It leads to a system of three equations in three unknowns that greatly reduces the computational burden. Finally, a case study has been reported. © 1991 Kluwer Academic Publishers.

1992 - Forward displacement analysis of parallel mechanisms: Closed form solution of prr-3s and ppr-3s structures [Articolo su rivista]
Parenti-Castelli, V.; Innocenti, C.
abstract

The forward displacement analysis (FDA) in closed form of two classes of new parallel mechanisms derived from the Stewart Platform Mechanism (SPM) is presented in this paper. These mechanisms, when a set of actuator displacements is given, become multiloop structures of type PRR-3S and PPR-3S, with P, R and S for prismatic, revolute and spherical pairs, whereas the SPM has the structure RRR- 3S. Solving the FDA in closed form means finding all the possible positions and orientations of the output controlled link when a set of actuator displacements is given, or equivalently, finding all possible closures of the corresponding structure. The closed form analysis of the PRR-3S and PPR-3S structures here presented results in algebraic equations in one unknown of degreee 16 and 12, respectively. Hence 16 and 12 closures of the corresponding structures can be obtained. Numerical examples confirm these new theoretical results. © 1992 by ASME.

1992 - Forward kinematics of the general 6-6 fully parallel mechanism: An exhaustive numerical approach via a mono-dimensional-search algorithm [Relazione in Atti di Convegno]
Innocenti, C.; Parenti-Castelli, V.
abstract

A new numerical method for the solution of the direct position analysis of the six d.o.f. fully parallel mechanism with general geometry. often referred to as generalized Stewart platform mechanism is presented. The main feature of the method, making it attractive with respect to the methods available in the 1 iterature, Is the ability to find out all the real so)utions of the direct position analysis. The effectiveness of the new algorithm relies upon the solution of only one equation in one unknown. That equation is strictly representative of the problem. 1 .e., it is free from extraneous roots and every solution of the direct position analysis entails the existence of a root for the equation. A case study is reported.

1992 - Forward kinematics of the general 6-6 fully parallel mechanism: an exhaustive numerical approach via a mono-dimensional-search algorithm [Relazione in Atti di Convegno]
Innocenti, C.; Parenti-Castelli, V.
abstract

1992 - Recursive determination of conjugate profiles in planar motion with application to gear design [Relazione in Atti di Convegno]
Innocenti, Carlo
abstract

A general procedure for determining the envelope of the outline of planar rigid figures is presented which allows both local and finite undercutting to be taken into account. A suitable parametrization of the enveloped curves, together with the insertion of cusps wherever undercutting occurs, enables the procedure to be applied recursively while maintaining high accuracy in describing the resulting envelopes. The proposed procedure provides the basis for an original validation method regarding parallel-axis spur and helical gears. The method takes into account possible undercutting during hobbing or shaping, considers the desired amount of meshing clearance over the entire tooth profile, and is able to detect meshing interference. Further, it provides a criterion in choosing the proper cutter profile. A numerical example showing the application of the method is discussed at the end of the paper.

1992 - Recursive determination of conjugate profiles in planar motion with application to gear design [Relazione in Atti di Convegno]
Innocenti, C.
abstract

A general procedure for determining the envelope of the outline of planar rigid figures is preseated which allows both local and finite undercutting to be taken into account. A suitable parametrization of the enveloped curves. together with the insertion of cusps wherever undercutting occurs, enables the procedure to be applied recursively while maintaining high accuracy in describing the resulting envelopes. The proposed procedure provides the basis for an original validat ion method regarding parallel-axis spur and helical gears. The method takes into account possible undercutting during hobbing or shaping. considers the desi red amount of meshing clearance over the entire tooth profile. and is able to detect meshing interference. Further, it provides a criterion in choosing the proper cutter profile. A numerical example showing the application of the method is discussed at the end of the paper.

1992 - Singularity-free evolution from one configuration to another in serial and fully-parallel manipulators [Relazione in Atti di Convegno]
Innocenti, C.; Parenti-Castelli, V.
abstract

Among the several ways adopted for the characterization of manipulator performances is identification of the typologies of maneuvers allowed by the manipulator kinematic arrangement. The multiplicity of configurations corresponding to a given hand position for serial manipulators, or to a given set of input values for fully-parallel manipulators, makes one wonder whether a manipulator can perform the maneuver of changing its configuration without meeting singularities. The paper shows that singularity-free configuration change is possible both for general-geometry serial and fully-parallel architectures. Results are reported that shed light on potential performances of manipulators and allow, in perspective, a deeper exploitation of their structural peculiarities.

1992 - Singularity-free evolution from one configuration to another in serial and fully-parallel manipulators [Relazione in Atti di Convegno]
Innocenti, C.; Parenti-Castelli, V.
abstract

Among the several ways adopted for the characterization of manipulator performances is identification of the typologies of maneuvers allowed by the manipulator kinematic arrangement. The multiplicity of configurations corresponding to a given hand position for serial manipulators, or to a given set of input values for fully-parallel manipulators. makes one wonder whether a manipulator can perform the maneuver of changing its configuration without meeting singularities. The paper shows that singularity-free configuration change IS possible both for general-geometry serial and fully-parallel architectures. Results are reported that shed light on potential performances of manipulators and allow. in perspective. a deeper exploitation of their structural peculiarities.

1990 - Direct position analysis of the Stewart platform mechanism [Articolo su rivista]
Innocenti, C.; Parenti-Castelli, V.
abstract

The direct position analysis of the Stewart platform mechanism (SPM), that is to find position and orientation of the platform when a set of actuator displacements is given, has been performed in closed-form. The analysis has been carried out by referring to a general kinematic model which has been derived on the basis of the characterization presented by Stewart. All the different SPM arrangements can be analysed in an unified way by this model. The analysis leads to a 16th order polynomial equation in one unknown from which 16 different positions and orientations of the platform can be derived. This new theoretical result is confirmed by numerical examples. © 1990.

1990 - Forward displacement analysis of parallel mechanisms. Closed form solution of PRR-3S and PPR-3S structures [Relazione in Atti di Convegno]
Parenti-Castelli, Vincenzo; Innocenti, Carlo
abstract

The forward displacement analysis (FDA) in closed form of two classes of new parallel mechanisms derived from the Stewart Platform Mechanism (SPM) is presented in this paper. These mechanisms, when a set of actuator displacements is given, become multi-loop structures of type PRR-3S and PPR-3S, with P, R and S for prismatic, revolute and spherical pairs, whereas the SPM has the structure RRR-3S. Solving the FDA in closed form means finding all the possible positions and orientations of the output controlled link when a set of actuator displacements is given, or equivalently, finding all possible closures of the corresponding structure. The closed form analysis of the PRR-3S and PPR-3S structures here presented results in algebraic equations in one unknown of degree 16 and 12 respectively. Hence 16 and 12 closures of the corresponding structures can be obtained. Numerical examples confirm these new theoretical results.

1986 - SINGULARITIES, CONFIGURATIONS, AND DISPLACEMENT FUNCTIONS FOR MANIPULATORS [Articolo su rivista]
Litvin, F. L.; Yi, Zhang; Parenti Castelli, V.; Innocenti, C.
abstract

A manipulator is considered as a system of rigid bodies interconnected by joints that permit relative motions with certain degrees of freedom. Nonlinear equations that relate the parameters of relative motions generally do not provide unique solutions, and consequently the bodies (links) of the mechanical system may form various configurations. The authors propose a method for determination of the configurations of this mechanical system and associated displacement functions that are based on the determination of singularities in motion of the mechanical system.

Università degli studi di Modena e Reggio Emilia

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