Auf Grund wachsender Nachfrage der simulativen Beurteilung von Getrieben hinsichtlich Geräuschentwicklung, Vibration und Belastbarkeit, kommt den Berechnungsmethoden immer größere Bedeutung zu. Hier spielen nicht nur die Steifigkeit der Verzahnung, sondern auch die Steifigkeiten der Wellen, Lagerungen und Gehäuse eine wichtige Rolle. Dazu werden unterschiedliche Simulationsmethoden vorgestellt und diese hinsichtlich Genauigkeit, Effizienz und Limitierung bewertet. Ein wichtiger Aspekt ist in diesem Zusammenhang auch die Modellbildung, insbesondere die Ermittlung der Eingabedaten für die Beschreibung der einzelnen Komponenten und deren Verbindungselemente. Die Koppelung des Mehrkörpersystems mit einem speziellen Auslegungstool für Getriebekomponenten ist neben der Multi-Physics-Simulation und der klassischen Mehrkörperdynamik eine Methode, die die Stärken beider Tools verbindet.

The development of forestry machines is currently heading towards new solutions that reduce their impact on the environment and in particular on the soft forest soil in which the machines operate. The terrain conditions that forestry machines encounter in their regular duties can be very rough, and if the vehicle-ground interaction is not properly controlled cumulative damage can progressively aggravate these conditions and potentially render a route or a zone impracticable, apart from causing a detrimental effect in the forest environment. In addition, new machine solutions must be considerably less damaging, both physically and mentally, to operators. There are certain imposed limits to the whole body vibrations to which industrial workers are exposed daily, which are very hard to fulfil in the context of wood harvesting operations with the current technological state of the machines. Chassis-suspended solutions in the market of forestry vehicles are practically inexistent. Multiple wheeled tracks and/or bogies are current solutions that improve dynamic performance and ground contact area of forestry vehicles, but they do not include suspension elements. Cab and seat suspensions are also used to reduce whole body vibrations, but they are only effective up to a certain degree, due to their relatively short stroke length and directional limitations. The implementation of chassis suspensions in forestry machines is therefore a very interesting open area of research in forestry technology. In this context the XT28, a forwarder prototype with active pendulum arm suspension, is currently being developed by Extractor AB in collaboration with Skogforsk; the Forestry Research Institute of Sweden. The present project focuses in analysis and comparison of the performance that active, semi-active and passive suspension systems with pendulum arm architecture would present, by studying their application in the XT28 machine. These systems have the potential to significantly improve forestry vehicle performance in terms of terrain friendliness and whole body vibrations over an unsuspended system. The task is carried out with the help of Multi-Body Dynamics simulation software along with other simulation and computational tools. Additionally, a general method to optimize and analyse forestry vehicle suspension performance is proposed and applied to the case of the XT28, which provides a fair and standardized way to compare the performance of the different suspensions. Keywords: Forestry machine, suspension, multi-objective optimization, forwarder, pendulum arm, active, semi-active, passive, XT28, Multibody Dynamics, soil-friendly, off-road. / Utvecklingen av skogsmaskiner är för närvarande på väg mot nya lösningar som minskar deras påverkan på miljön och i synnerhet på mjuk skogsmark. Skogsmaskinerna verkar ofta i mycket oländig och ojämn terräng, och om interaktionen mellan fordon och mark är alltför okontrollerad, så kan interaktionen ge upphov till kumulativa markskador som gradvis förvärras efter flera passager och eventuellt göra en rutt eller en zon oframkomlig, bortsett från att de orsaka skador på skogsmiljön. Dessutom måste nya maskinlösningar vara skonsammare, både fysiskt och mentalt, för förarna. Det finns nya gränser för maximala helkroppsvibrationer och maximala dagliga vibrationsdoser, som är mycket svåra att uppfylla vid skogsavverkning med dagens skogsmaskinsteknik. Chassidämpade lösningar är praktiskt taget obefintliga på dagens skogsmaskiner. Band och/eller boggier är aktuella lösningar som i viss mån förbättrar maskinernas dynamisk interaktion med marken, men de innehåller inga dämpelement, utan det är enbart däckens flexibilitet som ger maskinen en dämpfunktion. Hytt-och stolsdämpning används också för att minska helkroppsvibrationer, men de är endast effektiva till en viss grad, på grund av deras relativt korta slaglängd och riktningsbegränsningar. Införande av chassidämpning för skogsmaskiner är därför ett mycket intressant skogstekniskt forskningsområde. För närvarande utvecklas en skotare med aktivt dämpade pendelarmar av Extractor AB i samarbete med Skogforsk. Maskinen går under beteckningen XT28. Detta projekt fokuserar på att analysera och jämföra prestandan hos aktivt, semi-aktivt och passivt dämpade pendelarmlösningar, genom att implementera dessa i XT28-maskinen. Dessa system har potential att avsevärt förbättra skogsmaskinernas framkomlighet i oländig terräng och att minska helkroppsvibrationerna, jämfört med ofjädrade system. Uppgiften genomförs med hjälp av dynamiksimuleringsprogram i kombination med andra simulerings- och beräkningsverktyg. Dessutom föreslås en generell metodik för att optimera och analysera prestandan hos chassidämpningslösningar för skogsmaskiner. Metodiken tillämpas sedan på en XT28, som då, i detta fall, får fungera som en demonstrator för att jämföra prestandan hos olika chassidämplösningar. Nyckelord: Skogsmaskin, fjädring, optimering, skotare, pendelarm, aktiv, semi-aktiv, passiv, XT28, flerkroppsdynamik, markvänlig, off-road.

Pour mieux comprendre et traiter les troubles musculosquelettiques présents à l’épaule, une meilleure connaissance de la contribution et de la fonction de chaque muscle de l’articulation glénohumérale est nécessaire. L’analyse des forces musculaires et articulaires est une étape importante pour comprendre les mécanismes de blessures et les pathologies. Ces forces musculaires peuvent être estimées de façon non invasive grâce à des modèles musculosquelettiques. Le défi est de prédire de façon physiologique les trajectoires musculaires et les bras de levier afin de s’assurer d’avoir une cohérence des forces musculaires dans les modèles musculosquelettiques. L’objectif de cette thèse était d’améliorer la géométrie musculaire des modèles musculosquelettiques de l’épaule en passant par plusieurs méthodes différentes d’implémentation des trajectoires musculaires. À cet égard, nos objectifs spécifiques étaient de : (1) améliorer la géométrie musculaire des modèles multicorps rigides grâce à l’implémentation de contraintes transverses; (2) évaluer la fiabilité d’un modèle éléments finis pour l’estimation des bras de levier et (3) tester la sensibilité de la prédiction des bras de levier aux incertitudes sur les zones d’insertions musculaires; (4) établir une base de données de bras de levier 3D pour des mouvements de grande amplitude; (5) quantifier de façon expérimentale les changements architecturaux des muscles entre l’état au repos et différents niveaux de contraction isométrique. (1) Deux modèles multicorps rigides de la coiffe des rotateurs ont été développés : un modèle classique intégrant une représentation des lignes d’action en 1D et un modèle possédant des contraintes transverses entre les lignes d’action permettant une représentation 2D. La représentation 2D avec des contraintes transverses permet une représentation plus physiologique des trajectoires musculaires et des bras de levier que les modèles classiques 1D. Toutefois, lors de mouvement allant au-delà de 90° d’élévation du bras, lorsque les points d’origine et d’insertion se rapprochent, les bras de levier et les longueurs musculaires sont mal estimés, car le modèle ne prend pas en compte les déformations du volume musculaire. (2) Un modèle éléments finis a été développé à partir de données d’imagerie médicale. Ce modèle permet une estimation des bras de levier fidèle aux données d’IRM. Contrairement aux modèles multicorps rigides, notre modèle élément finis rend compte du fait qu’un même muscle peut avoir plusieurs actions selon la position de sa ligne d’action par rapport au centre de rotation de l’articulation. (3) Le modèle a également servi à faire une étude de sensibilité des bras de levier : les zones d’insertion des différents muscles de la coiffe des rotateurs et du deltoïde ont été déplacées et les bras de levier associés calculés. Les résultats montrent qu’une variation de 10 mm des points d’insertion sur la tête humérale peut amener un muscle à changer de fonction (par exemple adduction plutôt que d’abduction). (4) Une collecte de données expérimentales effectuées sur quatre épaules a permis de collecter les bras de levier du deltoïde et des muscles de la coiffe des rotateurs pour des mouvements de grande amplitude. Ces résultats permettent de mieux comprendre le rôle des muscles de l’articulation glénohumérale lors de la réalisation de différents mouvements. Le deltoïde antérieur a une grande action en flexion et en adduction; le deltoïde moyen est un fort abducteur; le deltoïde postérieur agit en extension. Contrairement au deltoïde, l’infra-épineux et le petit rond ont principalement une fonction de rotateur externe. (5) Une collecte de données impliquant 14 sujets a été réalisée dans le but de quantifier les changements de géométrie musculaire et d’angle de pennation associés à la contraction pour les muscles du biceps, triceps et deltoïde. Les angles de pennation ont été obtenus grâce à un système d’échographie et les changements de géométrie externe des muscles ont été mesurés grâce à un capteur de structure. Les résultats montrent que les changements architecturaux pour les muscles étudiés se produisent principalement entre 0 et 25% de contraction maximale volontaire (aucune différence significative observée entre 25 et 50%). Le muscle le plus affecté par les changements architecturaux est le biceps. Cette thèse a évalué différentes approches de modélisation de la géométrie musculaire : l’approche la plus bio-fidèle étant finalement la modélisation par éléments finis, car elle permet de prendre en compte les interactions entre les structures et les déformations musculaires. De plus, nous avons montré l’importance d’estimer avec rigueur les paramètres d’entrée (zones d’insertions musculaires) des modèles et de bien évaluer la bio-fidèlité des modèles développés avant de les utiliser dans des contextes cliniques. Dans ce but, de nouvelles données ont été acquises en termes de déformations musculaires et d’angle de pennation pour permettre l’évaluation de modèle intégrant de l’activation musculaire. / Understanding and treating musculoskeletal disorders of the shoulder requires additional knowledge of the contribution and function of each muscle of the glenohumeral joint. The analysis of muscle and joint forces is an important step in understanding injury mechanisms and pathologies. These muscle forces can be estimated non-invasively using musculoskeletal models. The challenge is to physiologically predict muscle trajectories and moment arms to ensure consistency of muscle forces in musculoskeletal models. The aim of this thesis was to improve muscle geometry in musculoskeletal models of the shoulder by testing several different techniques for implementing muscle trajectories. Our specific objectives were to: (1) improve muscle geometry of rigid multibody models by using transverse constraints; (2) assess the reliability of a finite element model for estimating moment arms and (3) evaluate the sensitivity of moment arm predictions to uncertainties in muscle insertion areas; (4) create a database of 3D moment arms for movements with high ranges of motion; (5) experimentally quantify muscles’ architectural changes between resting state and different levels of isometric contractions. (1) Two rigid multibody models of the rotator cuff were developed: a classic model representing muscles with lines of action in 1D and a 2D model with transverse constraints between lines of action of a single muscle. The 2D model (with transverse constraints) gives a more physiological representation of muscle trajectories and moment arms than the classical 1D model. However, for arm movements beyond 90° of elevation, when the origin and insertion points get closer, moment arms and muscle lengths are misestimated due to the mode’s inability to account for muscle volume deformations. (2) A finite element model of the glenohumeral joint was developed based on medical imaging. Moment arms were computed and compared to the literature and MRI data. Our finite element model produces moment arms consistent with the literature and MRI data. Unlike rigid multibody models, our finite element model accounts for the fact that one muscle can have several actions depending on the position of its line of action relative to the centre of rotation of the joint. (3) The model was used to study moment arm sensitivity: insertion areas of rotator cuff muscles and the deltoid were moved, and associated moment arms have been computed. Results showed that a 10 mm variation in insertion points on the humeral head could cause a muscle to change function (for example performing adduction rather than abduction). (4) The 3D moment arms were assessed on four post-mortem human surrogates during movements with high ranges of motion. Results of the study gave us a better understanding of muscle functions during different movements. The main findings of the study were that the anterior deltoid was the largest flexor and had an adduction component, the median deltoid was a strong abductor, and the posterior deltoid acted in extension. Unlike the deltoid, the infraspinatus and teres minor were the largest external rotators of the shoulder. (5) Experimental measurements were performed on 14 subjects in order to quantify changes in muscle geometry and pennation angles associated with different levels of contraction for the biceps, triceps and deltoid. Pennation angles were measured on subjects using a portable ultrasound system. External muscle deformations were measured with an iPad equipped with a structure sensor. Changes in muscle architecture for the biceps, triceps and deltoid during isometric contractions occurred mostly between 0 and 25% of maximal voluntary contraction (no significant difference was observed between 25 and 50%). Changes were higher for the biceps than other muscles. This thesis evaluated different approaches to model muscle geometry: the approach leading to the most physiological result was the finite element model due to modeling of the interactions between structure and muscle deformations. Additionally, we demonstrated the importance of rigorously estimating input parameters (muscle insertion areas) and of properly evaluating the bio-fidelity of the models developed before using them in clinical contexts. New data was acquired regarding muscle deformations and pennation angles to evaluate models integrating muscle activation.

Indiana University-Purdue University Indianapolis (IUPUI) / Belt-drives are used in many applications such as industrial machines, washing ‎machines, and accessory drives for automobiles and other vehicles. Multibody dynamics/finite ‎element numerical models have become an effective way to predict the dynamic response of ‎belt-drives. In this thesis, a high fidelity numerical model was built using a multibody ‎dynamics/finite element code to simulate a belt-drive. The belt-drive transmits power from a ‎turbine of a Rankin cycle (that uses the exhaust waste heat of the internal combustion engine as ‎heat source) to the crank shaft of the engine. The code uses a time-accurate explicit numerical ‎integration technique to solve the multibody dynamics differential equations. The belt was ‎modeled using three-node beam elements to account for the belt axial and bending ‎stiffness/damping, while the pulleys, shafts and tensioner body were modeled as rigid bodies. ‎The penalty technique was used to model normal contact between the belt and the pulleys. An ‎asperity-based friction model was used to approximate Coulomb friction between the belt and ‎the pulleys. The dynamic response predicted using the model was validated by comparing it to ‎experimental results supplied by Cummins Inc. A parameter sensitivity study was performed to ‎evaluate the change in response due to change in various belt-drive parameters. A fatigue ‎model was developed to predict the belt fatigue life using output from the explicit finite ‎element code including normal and tangential forces between the belt and the pulleys and belt ‎tension. The belt fatigue life was evaluated for alternative belt-drive configurations in order to ‎find the configuration with the longest life.‎

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A hydraulic damper plays an important role in tuning the handling and comfort characteristicsof a vehicle. Tuning and selecting a damper based on subjective evaluation, by considering theopinions of various users, would be an inefficient method since the comfort requirements of usersvary a lot. Instead, mathematical models of damper and simulation of these models in variousoperating conditions are preferred to standardize the tuning procedure, quantify the comfortlevels and reduce cost of testing. This would require a model, which is good enough to capture thebehaviour of damper in various operating and extreme conditions.The Force-Velocity (FV) curve is one of the most widely used model of a damper. This curve isimplemented either as an equation or as a look-up table. It is a plot between the maximum forceat each peak velocity point. There are certain dynamic phenomena like hysteresis and dependencyon the displacement of damper, which cannot be captured with a FV curve model, but are requiredfor better understanding of the vehicle behaviour.This thesis was conducted in cooperation with Volvo Cars with an aim to improve the existingdamper model which is a Force-Velocity curve. This work focuses on developing a damper model,which is complex enough to capture the phenomena discussed above and simple enough to beimplemented in real time simulations. Also, the thesis aims to establish a standard method toparameterise the damper model and generate the Force-Velocity curve from the tests performedon the damper test rig. A test matrix which includes the standard tests for parameterising andthe extreme test cases for the validation of the developed model will be developed. The final focusis to implement the damper model in a multi body simulation (MBS) software.The master thesis starts with an introduction, where the background for the project is described and then the thesis goals are set. It is followed by a literature review in which fewadvanced damper models are discussed in brief. Then, a step-by-step process of developing thedamper model is discussed along with few more possible options. Later, the construction of a testmatrix is discussed in detail followed by the parameter identification process. Next, the validationof the developed damper model is discussed using the test data from Volvo Hällered ProvingGround (HPG). After validation, implementation of the model in VI CarRealTime and Adams Caralong with the results are presented. Finally the thesis is concluded and the recommendations forfuture work are made on further improving the model. / En hydraulisk stötdämpare spelar en viktig roll för att fordonets hantering och komfort. Attjustera och välja en stötdämpare baserat på subjektiv utvärdering, genom att beakta olika användares åsikter, skulle vara en ineffektiv metod eftersom användarnas komfortkrav varierarmycket. Istället föredras matematiska modeller av stötdämpare och simulering av dessa modellerunder olika driftsförhållanden för att standardisera inställningsförfarandet, kvantifiera komfortnivåerna och minska testkostnaden. Detta skulle kräva en modell som är tillräckligt bra för attfånga upp stötdämparens beteende under olika drifts- och extrema förhållanden.Force-Velocity (FV) -kurvan är en av de mest använda stötdämparmodellerna. Denna kurvaimplementeras antingen som en ekvation eller som en uppslagstabell. Det är ett diagram somredovisar den maximala kraften vid varje maxhastighetspunkt. Det finns vissa dynamiskafenomen som hysteres och beroende av stötdämparens förskjutning, som inte kan fångas med enFV-kurvmodell, men som krävs för att bättre förstå fordonets beteende.Denna avhandling genomfördes i samarbete med Volvo Cars i syfte att förbättra den befintligastötdämparmodellen som är en Force-Velocity-kurva. Detta arbete fokuserar på att utveckla enstötdämparmodell, som är tillräckligt komplex för att fånga upp de fenomen som diskuteratsovan och tillräckligt enkel för att implementeras i realtidssimuleringar. Avhandlingen syftarockså till att upprätta en standardmetod för att parametrisera spjällmodellen och generera ForceVelocity-kurvan från de test som utförts på stötdämpartestriggen. En testmatris som innehållerstandardtest för parametrisering och extrema testfall för validering av den utvecklade modellenkommer att utvecklas. Det sista fokuset är att implementera stötdämparmodellen i en multi-bodysimulation (MBS) programvara.Examensarbetet inleds med en introduktion, där bakgrunden för projektet beskrivs ochdärefter definieras målen med arbetet. Det följs av en litteraturöversikt där några avanceradestötdämparmodeller diskuteras i korthet. Därefter diskuteras en steg-för-steg-process för attutveckla stötdämparmodeller tillsammans med några fler möjliga alternativ. Senare diskuteraskonstruktionen av en testmatris i detalj följt av parameteridentifieringsprocessen. Därefterdiskuteras valideringen av den utvecklade stötdämparmodellen med hjälp av testdata från VolvoHällered Proving Ground (HPG). Efter validering presenteras implementeringen av modellen iVI CarRealTime och Adams Car tillsammans med resultaten. Slutligen avslutas rapporten medslutsatser från arbetet och rekommendationer för framtida arbete görs för att ytterligare förbättramodellen.

This research effort develops a comprehensive computational framework to support the parametric optimal design of uncertain dynamical systems. Uncertainty comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; not accounting for uncertainty may result in poor robustness, sub-optimal performance and higher manufacturing costs. Contemporary methods for the quantification of uncertainty in dynamical systems are computationally intensive which, so far, have made a robust design optimization methodology prohibitive. Some existing algorithms address uncertainty in sensors and actuators during an optimal design; however, a comprehensive design framework that can treat all kinds of uncertainty with diverse distribution characteristics in a unified way is currently unavailable. The computational framework uses Generalized Polynomial Chaos methodology to quantify the effects of various sources of uncertainty found in dynamical systems; a Least-Squares Collocation Method is used to solve the corresponding uncertain differential equations. This technique is significantly faster computationally than traditional sampling methods and makes the construction of a parametric optimal design framework for uncertain systems feasible. The novel framework allows to directly treat uncertainty in the parametric optimal design process. Specifically, the following design problems are addressed: motion planning of fully-actuated and under-actuated systems; multi-objective robust design optimization; and optimal uncertainty apportionment concurrently with robust design optimization. The framework advances the state-of-the-art and enables engineers to produce more robust and optimally performing designs at an optimal manufacturing cost. / Ph. D.

Tracked vehicles are designed to operate in various terrains, ranging from soft mud to hard tarmac. This wide range of terrains presents significant challenges for the suspension system, as its components must be suitable for all types of terrain. The selection of these components is crucial for minimizing acceleration levels within the vehicle, ensuring that personnel can comfortably endure extended durations inside. BAE Systems Hägglunds AB develops and produces an armored tracked vehicle called the CV90. Within the CV90’s suspension system, a key component known as the torsion bar, a rotational spring, plays a primary role in reducing the vehicle’s motion. The CV90 vehicle has seven wheels on each side, with each wheel having its dedicated torsion bar. To measure the whole-body vibration experienced within the vehicle, a measurement called the Vibrational Dose Value (VDV) is utilized. The main objective of this thesis is to develop a data-driven model to optimize the suspension system by identifying the combination of torsion bars that generates the smallest VDV. The data used for optimization is based on simulations of the CV90 vehicle in a virtual environment. In the simulation, the CV90 vehicle, with its full dynamics, is driven over a specific virtual road at a particular velocity. The simulation itself cannot be manipulated; only the input values can be adjusted. Thus, we consider the simulation as a black box, which led us to implement the black-box optimization algorithm known as Particle-Swarm. In this thesis, four different roads, each with velocities ranging from four to seven different levels, were provided to the optimization model. The results show that the model identifies a combination of torsion bars that generates a small VDV for all combinations of velocities and roads, with an average VDV improvement of around 20% - 60% compared to a reference case. Since this thesis serves as a proof of concept, the conclusion is that the devised method is effective and suitable for addressing the problem at hand. Nonetheless, for seamless integration of this method into the tracked vehicle development process, further research is necessary.

Nous nous intéressons à la conception des mains mécaniques anthropomorphes destinées à manipuler des objets dans un environnement humain. Via l'analyse du mouvement de sujets humains lors d'une tâche de manipulation de référence, nous proposons une méthode pour évaluer la capacité des mains robotiques à manipuler les objets. Nous montrons comment les rapports de couplage angulaires entre les articulations et les limites articulaires, influent sur l'aptitude à manipuler dynamiquement des objets. Nous montrons également l'impact du poignet sur les tâches de manipulation rapides. Nous proposons une stratégie pour calculer les forces de manipulation en bout de doigts et dimensionner les moteurs d'un tel préhenseur. La méthode proposée est dépendante de la tâche visée et s'adapte à tout type de mouvement dès lors qu'il peut être capturé et analysé. Dans une deuxième partie, consacrée aux robots manipulateurs, nous élaborons des algorithmes de commande optimale. En considérant l'énergie cinétique du robot comme une métrique, le modèle dynamique est formulé sous forme tensorielle dans le cadre de la géométrie Riemannienne. La discrétisation temporelle est basée sur les Éléments Finis d'Hermite. Nous intégrons les équations de Lagrange du mouvement par une méthode de perturbation. Des exemples de simulation illustrent la superconvergence de la technique d'Hermite. Le critère de contrôle est choisi indépendant des paramètres de configuration. Les équations de la commande associées aux équations du mouvement se révèlent covariantes. La méthode de commande optimale proposée consiste à minimiser la fonction objective correspondant au critère invariant sélectionné. / We focus on the design of anthropomorphous mechanical hands destined to manipulate objects in a human environment. Via the motion analysis of a reference manipulation task performed by human subjects, we propose a method to evaluate a robotic hand manipulation capacities. We demonstrate how the angular coupling between the fingers joints and the angular limits affect the hands potential to manipulate objects. We also show the influence of the wrist motions on the manipulation task. We propose a strategy to calculate the fingertip manipulation forces and dimension the fingers motors. In a second part devoted to articulated robots, we elaborate optimal control algorithms. Regarding the kinetic energy of the robot as a metric, the dynamic model is formulated tensorially in the framework of Riemannian geometry. The time discretization is based on the Hermite Finite Elements.A time integration algorithm is designed by implementing a perturbation method of the Lagrange's motion equations. Simulation examples illustrate the superconvergence of the Hermite's technique. The control criterion is selected to be coordinate free. The control equations associated with the motion equations reveal to be covariant. The suggested control method consists in minimizing the objective function corresponding to the selected invariant criterion.

Este trabalho tem como objetivo estudar a influência da geometria de suspensão do veículo nas atitudes da massa suspensa. Apresenta um confronto entre obras e autores e está segmentada em três partes; onde na primeira parte são definidos os conceitos básicos como dive, squat, lift, anti-dive, anti-squat, anti-lift e equivalente trailing-arm; na segunda parte são apresentadas as limitações e os novos conceitos definidos por R. S. Sharp e na terceira parte é apresentado o modelo dinâmico bidimensional introduzido por Fu-Cheng Wang. Apresenta um modelo virtual em sistema de multi-corpos desenvolvido no programa ADAMS, com todos os subsistemas que compõe um veículo completo. Inova ao trazer como objeto de estudo um veículo de competição (fórmula SAE) que possui como particularidade o sistema de suspensão push-rod. Surpreende com os resultados obtidos, pois, contrariam os conceitos básicos encontrados na maioria dos livros / This work has objective study the influence of suspension geometry on the sprung mass attitudes. It presents a confrontation among works and authors and this segmented in three parts; where in the first part the basic concepts are defined, dive, squat, lift, anti-dive, anti-squat, anti-lift and equivalent trailing-arm; in the second part the limitations are presented and the new concepts are defined for R. S. Sharp and in the third part are presented the bidimensional dynamic model introduced by Fu-Cheng Wang. It presents a virtual model in system of multi-bodies developed in the program ADAMS, with all the subsystems that composes a complete vehicle. It innovates when bringing such object to study one vehicle of competition (formula SAE) that it has a particularity suspension system push-rod. It surprises with results because it’s opposite of the basic concepts which is present in the majority of books