
Carlo INNOCENTI
Professore Ordinario Dipartimento di Ingegneria "Enzo Ferrari"

Home 
Curriculum(pdf) 
Didattica 
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 fivemeasurement 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
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 fivemeasurement 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.
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 twopulley synchronous belt transmission connecting, with no belt tensioner, two parallelaxis shafts with a variable velocity ratio. The procedure takes into account the limited number of choices for pitch and length of offtheshelf synchronous belts, which translates into the need of fineadjusting 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 onedegreeoffreedom machine whose nonstationary parts move parallel to the same plane. Differently from the wellknown 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 twoshaft device. An example shows application of the proposed method to a fourcylinder inline 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 crossedaxis 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 rigidbody 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 crossedaxis, 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 endeffector 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 specialgeometry manipulator transforms into a generalgeometry 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
The paper is aimed at finding all relative rigidbody 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.
2006
 Designing synchronous belt transmissions with variable velocity ratio
[Relazione in Atti di Convegno]
Innocenti, C.; Paganelli, D.
abstract
The paper presents a new procedure to design a twopulley synchronous belt transmission connecting, with no belt tensioner, two parallelaxis shafts with a variable velocity ratio. The procedure takes into account the limited number of choices for pitch and length of offtheshelf synchronous belts, which translates into the need of fineadjusting 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. Copyright © 2006 by ASME.
2006
 Optimal choice of the shaft angle for involute gear hobbing
[Relazione in Atti di Convegno]
Innocenti, C.
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 crossedaxis 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. Copyright © 2006 by ASME.
2006
 Position Analysis of the RRP3(SS) MultiLoop 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 28thorder 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 wellknown inparallelactuated spatial manipulator.Numerical examples show adoption of the proposed method in dealing with two case studies.
2005
 Positioning the base of spatial 2dof regional manipulators in order to reach as many arbitrarilychosen 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 endeffector 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 rigidbody position of the base of twodegreeoffreedom (2dof) manipulators  either serial or fullyparallel  in order to enable them to accomplish the abovementioned task. Numerical examples are reported. © 2005 IEEE.
2004
 Position analysis of the RRP3(SS) multiloop 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 28thorder 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 wellknown inparallelactuated 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 rigidbody 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 clearancefree idealization of the structure under investigation. An example shows application of the proposed method to the analysis of the structure derived from a multiloop 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 generalgeometry 66 fullyparallel manipulator. The forty solutions that the problem at hand admits in the complex domain are found by determining the roots of a 40thorder univariate polynomial equation. Unlike the existing algorithm, the proposed one is suitable for implementation in a standard floatingpoint 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 rigidbody 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 clearancefree idealization of the structure under investigation. An example shows application of the proposed method to the analysis of the structure derived from a multiloop manipulator by freezing its actuators.
1998
 Closedform determination of the location of a rigid body by seven inparallel 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 soughtfor rigidbody location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fullyparallel 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 66 fullyparallel manipulator. The forty solutions that the problem at hand admits in the complex domain are found by determining the roots of a 40thorder univariate polynomial equation. Unlike the existing algorithm, the proposed one is suitable for implementation in a standard floatingpoint computation environment. A numerical example shows application of the new algorithm to a case study.
1998
 Singularityfree evolution from one configuration to another in serial and fullyparallel manipulators
[Articolo su rivista]
Innocenti, C.; ParentiCastelli, 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 singularityfree configuration change is possible both for generalgeometry serial and fullyparallel 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 7link assur kinematic chain featuring one ternary link connected to ternary links only
[Articolo su rivista]
Innocenti, C.
abstract
The paper presents the analyticalform position analysis of one of the three existing 7link 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 multidegreeof freedom gear trains
[Articolo su rivista]
Innocenti, C.
abstract
The paper proposes a new approach to the efficiency evaluation of any one or multidegreeoffreedom gear trains. The suggested approach generalizes the known procedures developed for twodegreeoffreedom 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
 Closedform determination of the location of a rigid body by seven inparallel linear transducers
[Relazione in Atti di Convegno]
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 soughtfor rigidbody location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fullyparallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.
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 64 fullyparallel mechanism
[Articolo su rivista]
Innocenti, C.
abstract
This paper presents the direct position analysis of the fullyparallel 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 specificallydeveloped elimination scheme, the closure equation set is reduced to a 32ndorder algebraic equation with only one unknown, which proves free from extraneous roots. Hence 32 closure configurations of the 64 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 arbitrarilychosen rigidbody positions. Core of the proposed method is an original algebraic elimination procedure that allows five unknowns to be dropped from a set of six secondorder 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 7link 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 7link Assur kinematic chains, this paper presents the algebraicform position analysis of the remaining 7link 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 fourbar linkages intersect each other at 18 real points at most. Finally, a numerical example shows application of the new theoretical results. © 1995.
1994
 Analyticalform position analysis of the 7link assur kinematic chain with four seriallyconnected ternary links
[Articolo su rivista]
Innocenti, C.
abstract
The paper addresses the position analysis of the 7link Assur kinematic chain that features three binary links and four seriallyconnected 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 endeffector with six coplanar spherical joints constrained to lie on xy sliding tables. By properly controlling the postures of the sliding tables, the endeffector 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 endeffector 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 eighthorder 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; ParentiCastelli, Vincenzo
abstract
The direct position analysis of fullyparallel manipulators entails in essence the analysis of fullyparallel 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 fullyparallel kinematic chains. The enumeration leads to the identification of twentyone different fullyparallel kinematic chains and provides the frame within which the state of the art in the field of direct position analysis of fullyparallel manipulators  or, more strictly, of fullyparallel 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 singledegreeoffreedom 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 stickslip 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 arbitrarilychosen rigidbody positions. Core of the proposed method is an original algebraic elimination procedure that allows five unknowns to be dropped from a set of six secondorder 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 rigidbody positions. Core of the proposed method is an original algebraic elimination procedure that allows five unknowns to be dropped from a set of six secondorder 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 44 fully inparallel actuated six degreeoffreedom mechanism
[Relazione in Atti di Convegno]
Innocenti, C.; ParentiCastelli, V.
abstract
This paper presents the direct position analysis in analytical form of a sixdegreeoffreedom 44 fullyparallel 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 tetrahedronlike 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 44 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 44 structure is sixteen. Numerical examples are reported which illustrate and confirm the new theoretical result.
1993
 Closedform direct position analysis of a 55 parallel mechanism
[Articolo su rivista]
Innocenti, C.; ParentiCastelli, V.
abstract
The paper presents the closed form direct displacement analysis for a class of Stewart platformtype 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 fullyparallel spherical wrist
[Articolo su rivista]
Innocenti, C.; ParentiCastelli, V.
abstract
This paper presents the echelon form direct position analysis of a class of fully inparallel 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 fullyparallel arrangement. The analysis results in a twoequation 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 66 fully parallel mechanism: An exhaustive numerical approach via a monodimensionalsearch algorithm
[Articolo su rivista]
Innocenti, C.; ParentiCastelli, 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.; ParentiCastelli, 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 nonlinear 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 prr3s and ppr3s structures
[Articolo su rivista]
ParentiCastelli, 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 PRR3S and PPR3S, 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 PRR3S and PPR3S 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 66 fully parallel mechanism: An exhaustive numerical approach via a monodimensionalsearch algorithm
[Relazione in Atti di Convegno]
Innocenti, C.; ParentiCastelli, 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 66 fully parallel mechanism: an exhaustive numerical approach via a monodimensionalsearch algorithm
[Relazione in Atti di Convegno]
Innocenti, C.; ParentiCastelli, 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.
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 parallelaxis 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 parallelaxis 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
 Singularityfree evolution from one configuration to another in serial and fullyparallel manipulators
[Relazione in Atti di Convegno]
Innocenti, C.; ParentiCastelli, 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 singularityfree configuration change is possible both for generalgeometry serial and fullyparallel architectures. Results are reported that shed light on potential performances of manipulators and allow, in perspective, a deeper exploitation of their structural peculiarities.
1992
 Singularityfree evolution from one configuration to another in serial and fullyparallel manipulators
[Relazione in Atti di Convegno]
Innocenti, C.; ParentiCastelli, 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 singularityfree configuration change IS possible both for generalgeometry serial and fullyparallel 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.; ParentiCastelli, 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 closedform. 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 PRR3S and PPR3S structures
[Relazione in Atti di Convegno]
ParentiCastelli, 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 multiloop structures of type PRR3S and PPR3S, with P, R and S for prismatic, revolute and spherical pairs, whereas the SPM has the structure RRR3S. 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 PRR3S and PPR3S 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.