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In this investigation, generalized Newton-Euler equations are developed for deformable bodies that undergo large translational and rotational displacements. The configuration of the deformable body is identified using coupled sets of reference and elastic variables. The nonlinear generalized Newton-Euler equations are formulated in terms of a set of time invariant scalars and matrices that depend on the spatial coordinates as well as the assumed displacement field. These time-invariant quantities appear in the nonlinear terms that represent the dynamic coupling between the rigid body modes and the elastic deformation. A set of recursive kinematic equations, in which the absolute accelerations are expressed in terms of the joint and elastic accelerations are developed for several joint types. The recursive kinematic equations and the joint reaction relationships are combined with the generalized Newton-Euler equations in order to obtain a system of loosely coupled equations which have sparse matrix structure. Using matrix partitioning and recursive projection techniques based on optimal block factorization an order n solution for the system equations is obtained.... Multibody systems, Deformable bodies, Newton-Euler equations, Elastic deformation, Kinematic equations.

In this investigation, generalized Newton-Euler equations are developed for deformable bodies that undergo large translational and rotational displacements. The configuration of the deformable body is identified using coupled sets of reference and elastic variables. The nonlinear generalized Newton-Euler equations are formulated in terms of a set of time invariant scalars and matrices that depend on the spatial coordinates as well as the assumed displacement field. These time-invariant quantities appear in the nonlinear terms that represent the dynamic coupling between the rigid body modes and the elastic deformation. A set of recursive kinematic equations, in which the absolute accelerations are expressed in terms of the joint and elastic accelerations are developed for several joint types. The recursive kinematic equations and the joint reaction relationships are combined with the generalized Newton-Euler equations in order to obtain a system of loosely coupled equations which have sparse matrix structure. Using matrix partitioning and recursive projection techniques based on optimal block factorization an order n solution for the system equations is obtained.... Multibody systems, Deformable bodies, Newton-Euler equations, Elastic deformation, Kinematic equations.

The state of the art dynamic response analysis of flexible multibody systems is currently restricted to elastic bodies with homogeneous materials. The requirements for high speed operation has made it necessary to use lightweight multi layered composite bodies in robotic systems and space structure applications. Dynamic modeling and analysis of such systems are particularly important since the effects of body flexibility to the performance are likely to be more pronounced. The eight-noded isoperimetric quadrilateral element with independent rotational and displacement degrees of freedom is extended to laminated composite elements. The element includes an arbitrary number of bonded layers, each of which may have a different thickness. The transverse shear deformation which is a predominant factor in the analysis of laminated composite structures is taken into account in developing the stiffness and mass matrices. The corresponding 3-D mode shapes are then incorporated to the multibody system dynamical equations. Floating body reference frames allow the selection of different boundary conditions, and the dynamical equations contain all the nonlinear interactions between the rigid and elastic motion. Example simulations are presented to illustrate the methods proposed.

460p. ; 25cm

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Understanding the behavior and performance of engineering applications like machines, transport machines, manipulators, and mechanisms like gears relies heavily on the study of the dynamics and kinematics of complex mechanical systems. This article provides a comprehensive overview of recent findings and advancements in this field. The purpose of this work is to provide an in-depth introduction to the theoretical and practical considerations involved in assessing the dynamic and kinematic properties of such complex systems. Understanding forces, torques, displacements, and velocities is highlighted as crucial to the design and study of complex mechanical systems, and the underlying mathematical models and concepts that control their motion are investigated. This paper also evaluates and critiques the most current developments in modeling and simulation approaches such as finite element analysis (FEA), computational dynamics, and optimization strategies. The multidisciplinary aspect of the topic and its potential to progress numerous engineering, robotics, and industrial applications constitute the topic's scientific uniqueness. The results include various advanced modeling and simulation techniques like FEA, computational dynamics, and multibody dynamics simulation. In conclusion, this article compiles a lot of information on the dynamics and kinematics of sophisticated mechanical systems, such as machines, transport machines, manipulators, and mechanisms.

Understanding the behavior and performance of engineering applications like machines, transport machines, manipulators, and mechanisms like gears relies heavily on the study of the dynamics and kinematics of complex mechanical systems. This article provides a comprehensive overview of recent findings and advancements in this field. The purpose of this work is to provide an in-depth introduction to the theoretical and practical considerations involved in assessing the dynamic and kinematic properties of such complex systems. Understanding forces, torques, displacements, and velocities is highlighted as crucial to the design and study of complex mechanical systems, and the underlying mathematical models and concepts that control their motion are investigated. This paper also evaluates and critiques the most current developments in modeling and simulation approaches such as finite element analysis (FEA), computational dynamics, and optimization strategies. The multidisciplinary aspect of the topic and its potential to progress numerous engineering, robotics, and industrial applications constitute the topic's scientific uniqueness. The results include various advanced modeling and simulation techniques like FEA, computational dynamics, and multibody dynamics simulation. In conclusion, this article compiles a lot of information on the dynamics and kinematics of sophisticated mechanical systems, such as machines, transport machines, manipulators, and mechanisms.

Understanding the behavior and performance of engineering applications like machines, transport machines, manipulators, and mechanisms like gears relies heavily on the study of the dynamics and kinematics of complex mechanical systems. This article provides a comprehensive overview of recent findings and advancements in this field. The purpose of this work is to provide an in-depth introduction to the theoretical and practical considerations involved in assessing the dynamic and kinematic properties of such complex systems. Understanding forces, torques, displacements, and velocities is highlighted as crucial to the design and study of complex mechanical systems, and the underlying mathematical models and concepts that control their motion are investigated. This paper also evaluates and critiques the most current developments in modeling and simulation approaches such as finite element analysis (FEA), computational dynamics, and optimization strategies. The multidisciplinary aspect of the topic and its potential to progress numerous engineering, robotics, and industrial applications constitute the topic's scientific uniqueness. The results include various advanced modeling and simulation techniques like FEA, computational dynamics, and multibody dynamics simulation. In conclusion, this article compiles a lot of information on the dynamics and kinematics of sophisticated mechanical systems, such as machines, transport machines, manipulators, and mechanisms.

Understanding the behavior and performance of engineering applications like machines, transport machines, manipulators, and mechanisms like gears relies heavily on the study of the dynamics and kinematics of complex mechanical systems. This article provides a comprehensive overview of recent findings and advancements in this field. The purpose of this work is to provide an in-depth introduction to the theoretical and practical considerations involved in assessing the dynamic and kinematic properties of such complex systems. Understanding forces, torques, displacements, and velocities is highlighted as crucial to the design and study of complex mechanical systems, and the underlying mathematical models and concepts that control their motion are investigated. This paper also evaluates and critiques the most current developments in modeling and simulation approaches such as finite element analysis (FEA), computational dynamics, and optimization strategies. The multidisciplinary aspect of the topic and its potential to progress numerous engineering, robotics, and industrial applications constitute the topic's scientific uniqueness. The results include various advanced modeling and simulation techniques like FEA, computational dynamics, and multibody dynamics simulation. In conclusion, this article compiles a lot of information on the dynamics and kinematics of sophisticated mechanical systems, such as machines, transport machines, manipulators, and mechanisms.

A method of the spatial kinematic and dynamic analysis of deformable multibody systems subject to topology changes and impacts is presented. A pieced interval analysis scheme that accounts for the change in the spatial system topology due to the changes on the connectivity between bodies is developed. Deformable bodies in the system are discretized using the finite element method and accordingly a finite set of deformation modes is employed to characterize the system vibration. Even though there are infinitely many arrangements for deformable body axes, computational difficulties may be encountered due to the use of a limited number of deformation modes. Therefore, the deformable body references have to be carefully selected, and accordingly as the system topology changes, new bases for the configuration space to another, a set of spatial interface conditions or compatibility conditions that are formulated using a set of nonlinear algebraic equations are developed. The solution of these equations uniquely define the spatial configuration of the deformable multibody system after the change in the system kinematic structure. The techniques proposed in this research are applied to several technological system such as robotic manipulators and weapon systems. Keywords: Spatial kinematics; Dynamic analysis; Deformable multibody systems; Interval analysis scheme; Nonlinear algebraic equations.

Conventionally kinematical constraints in multibody systems are treated similar to geometrical constraints and are modeled by constraint reaction forces which are perpendicular to constraint surfaces. However, in reality, one may want to achieve the desired kinematical conditions by control forces having different directions in relation to the constraint surfaces. The conventional equations of motion for multibody systems subject to kinematical constraints are generalized by introducing general direction control forces. Conditions for the selections of the control force directions are also discussed. A redundant robotic system subject to prescribed end-effector motion is analyzed to illustrate the methods proposed.

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The Phillips Laboratory at Edwards AFB has constructed a test bed for the validation and comparison of modeling and control theories for the dynamics and control of flexible multibody systems. This project is called the Planar Articulating Controls Experiment (PACE). This paper presents the experimental apparatus for PACE and the problem formulation. An in-depth analysis on DC motor dynamics was also performed.