Floating Frame Of Reference Research Articles

Dynamic Simulation and Collision Detection for Flexible Mechanical Systems with Contact Using the Floating Frame of Reference Formulation

Abstract Contact simulation is essential in modelling mechanical systems. The contact models require accurate geometric information, which is determined through collision detection methods. When the mechanical system includes flexible bodies such as structural components, the dynamic formulation and collision detection can be more challenging, as the geometric boundaries of such components keep changing during the simulation. The floating frame of reference (FFR) formulation is suitable for flexible systems with small deformation. In this work, a stable and efficient dynamic simulation method is introduced for flexible systems with contact based on the FFR formulation. In addition, a curve-based collision detection method is proposed, which is more consistent with the dynamic formulation and more efficient than common existing collision detection methods. Case studies of flexible beams and multibody systems are employed to demonstrate the performance of the proposed dynamic simulation and collision detection methods.

Free vibration analysis of a rotating skew plate by using the absolute nodal coordinate formulation

The skew angle is an important feature for the rotating plate, which has a significant influence on the modal characteristics of the vibration. However, the variation of modal properties induced by the skew angle for a rotating cantilever plate has seldom been studied, and most work has been focused on the static behaviors or free vibration analysis of non-rotating skew plates in the existing literature. A novel dynamic model using a floating frame of reference (FFR) based on the absolute nodal coordinate formulation (ANCF) shell element is proposed to investigate the vibration behaviors of a rotating skew plate. The convergence and validation analyses are performed, and the results obtained by the present method are verified by comparing with those in the available literature. A detailed parameters investigation on the effects of skew angle, aspect ratio, hub radius and stagger angle on the variations of modal characteristics are demonstrated. The eigenvalue loci veering phenomena along with the corresponding mode shape variations are presented and comprehensively discussed. In addition, it is found that the skew plate may buckle due to the non-uniform centrifugal force, which leads to the zero fundamental frequency by the critical rotational speed.

Nonlinear Torsional Stiffness Analysis of Harmonic Drives Using Flexible Multibody Dynamics Simulation

Predicting the nonlinear torsional stiffness of harmonic drives is important not only for system control but also for the further development of the drive. However, it is difficult to predict the torsional stiffness because of the elastic deformation of the flexspline and the many contacts involved. Furthermore, nonlinear dynamic contact simulations between the elastic components of the harmonic drive are disadvantaged by high computational burden and convergence problems. To address these challenges, we establish a flexible multibody modeling process using augmented formulations of a floating reference frame to simulate the operation of the harmonic drive. The elastic deformation of the flexspline and the dynamic contacts between the main components are considered in the reproduction of the contact mechanism of the drive. Coordinate reduction techniques are used to properly replicate an elastic shaft, enabling the effective simulation of flexible multibody dynamics, including nonlinear elastic tooth contact analysis. The performance of the proposed modeling process is evaluated using catalog and experimental data on two types of standard harmonic drives (SHG-25-100-UH and SHG-40-100-UH). The hysteresis curve is predicted through flexible multibody dynamics simulation and the accuracy of parameters of torsional stiffness is approximately 91.7% on average. The proposed modeling method can be improved to predict other measures of performance and it remains a potential research topic.

Research on vibration suppression and trajectory tracking control strategy of a flexible link manipulator

Residual vibrations caused by point-to-point motions reduce the positioning accuracy and dynamic performance of flexible link manipulators, and the trajectory planning method, a well-known open-loop control strategy, has been proven to effectively suppress the residual vibration in point-to-point motion. However, this open-loop control method has limitations in dealing with model uncertainty and disturbance problems. In this paper, a control strategy based on dynamics-based trajectory planning and fuzzy self-tuning PD (FST PD) controller is proposed, and applied to achieve residual vibration suppression and trajectory tracking of a flexible link manipulator. To improve the trajectory tracking performance under external disturbances, this control strategy is combined with a linear extended state observer (LESO). Firstly, the dynamic model of the system is deduced using the floating reference frame and Lagrange equation. On this basis, the objective function to minimize the lateral deformation of the tip is constructed, and then the optimal trajectory is obtained by using the Crossbreeding PSO (CBPSO) algorithm. Secondly, the optimal trajectory is used as the desired trajectory to suppress residual vibration, and the FST PD controller combined with the LESO is used to achieve high-precision trajectory tracking control of the flexible link manipulator. Finally, the effectiveness and feasibility of the composite control strategy is verified through multiple simulations. The proposed method can provide support for vibration suppression of flexible link manipulators; meanwhile, the controller structure of this method is simple and easy to implement, and the use of sensors/actuators and other equipment in the system is reduced, which effectively reduces the economic cost.

Actuation and Motion Control of Flexible Robots: Small Deformation Problem

AbstractThis paper introduces a new computational approach for the articulated joint/deformation actuation and motion control of robot manipulators with flexible components. Oscillations due to small deformations of relatively stiff robot components which cannot be ignored, are modeled in this study using the finite element (FE) floating frame of reference (FFR) formulation which employs two coupled sets of coordinates: the reference and elastic coordinates. The inverse dynamics, based on the FFR formulation, leads to driving forces associated with the deformation degrees of freedom. Because of the link flexibility, two approaches can be considered to determine the actuation forces required to achieve the desired motion trajectories. These two approaches are the partially constrained inverse dynamics (PCID) and the fully constrained inverse dynamics (FCID). The FCID approach, which will be considered in future investigations and allows for motion and shape control, can be used to achieve the desired motion trajectories and suppress undesirable oscillations. The new small-deformation PCID approach introduced in this study, on the other hand, allows for achieving the desired motion trajectories, determining systematically the actuation forces and moments associated with the robot joint and elastic degrees of freedom, and avoiding deteriorations in the vibration characteristics as measured by the differences between the inverse- and forward-dynamics solutions. A procedure for determining the actuation forces associated with the deformation degrees of freedom is proposed and is exemplified using piezoelectric actuators. The PCID solution is used to define a new set of algebraic equations that can be solved for the piezoelectric actuation voltages required to maintain the forward-dynamics oscillations within their inverse-dynamics limits. A planar two-link flexible-robot manipulator is presented to demonstrate the implementation of the joint/deformation actuation approach. The results obtained show deterioration in the robot precision if the deformation actuation is not considered.

Near-elimination of small oscillations of articulated flexible-robot systems

This paper proposes a new hybrid actuation system for near-elimination of the small oscillations of articulated flexible-robot systems (AFRS). The hybrid actuation control forces are obtained by solving a fully-constrained inverse-dynamics (FCID) problem of relatively stiff robots experiencing small deformations, which lead to deterioration of their performance and precision. The FCID procedure is based on the floating frame of reference (FFR) formulation that allows for systematically determining the actuation forces associated with deformation modes. By using the resulting FCID algebraic equations, numerical integration of the equations of motion to determine the AFRS actuation forces can be avoided. This paper summarizes the new motion/shape control strategy to be used and defines problems to be addressed in more detailed future investigations.

A geometrically accurate deformable-body approach for the analysis of robotic and parallel-mechanism systems

Strength and durability investigations of parallel-mechanism (PM) and robotic systems, used as integral part in modern manufacturing, are necessary at the virtual design stage. Nonetheless, because of the limitations of existing finite element (FE) approaches, flexible-link geometries are often simplified or distorted when converting solid models to FE analysis meshes. This article introduces and demonstrates the use of a new unified geometry/analysis approach for the small-deformation analysis of robotic and parallel mechanism (RPM) systems with flexible links. The approach used in this investigation integrates the geometrically accurate absolute nodal coordinates formulation (ANCF) with the computationally efficient floating frame of reference (FFR) formulation that allows for systematic elimination of high-frequency and insignificant deformation modes. The proposed ANCF/FFR approach allows modeling accurately the stress-free reference configuration geometry, captures the dynamic coupling between the rigid-body and elastic displacements, is based on a unified geometry/analysis mesh that eliminates the need for geometry/analysis model conversion or coordinate transformation, and allows for efficient and accurate solution of the nonlinear dynamic equations that govern the RPM motion. The formulation of the spatial ANCF/FFR equations of motion including the elastic (stress) forces using a general continuum-mechanics approach is presented, and use of the strain split method (SSM) as an FE locking-alleviation technique is discussed. A frequency-convergence analysis of flexible links with tapered geometry is performed and the obtained numerical results are compared with solutions obtained using commercial FE software. The application of the new procedure in the nonlinear dynamics simulations of RPM systems is demonstrated using a spatial parallel mechanism that includes flexible links and prismatic, revolute, and spherical joints.

The effects of blade structural model fidelity on wind turbine load analysis and computation time

Abstract. Aero-servo-elastic analyses are required to determine the wind turbine loading for a wide range of load cases as specified in certification standards. The floating reference frame (FRF) formulation can be used to model the structural response of long and flexible wind turbine blades. Increasing the number of bodies in the FRF formulation of the blade increases both the fidelity of the structural model and the size of the problem. However, the turbine load analysis is a coupled aero-servo-elastic analysis, and computation cost not only depends on the size of the structural model, but also depends on the aerodynamic solver and the number of iterations between the solvers. This study presents an investigation of the performance of the different fidelity levels as measured by the computational cost and the turbine response (e.g., blade loads, tip clearance, tower-top accelerations). The analysis is based on aeroelastic simulations for normal operation in turbulent inflow load cases as defined in a design standard. Two 10 MW reference turbines are used. The results show that the turbine response quickly approaches the results of the highest-fidelity model as the number of bodies increases. The increase in computational costs to account for more bodies can almost entirely be compensated for by changing the type of the matrix solver from dense to sparse.

Dynamics analysis of spatial parallel robot with rigid and flexible links.

To analyze the rigid-flexible coupling effects on the dynamic performance of a robot system, a dynamic model of a parallel robot with flexible spatial links is derived in detail using a floating frame of reference (FFR) formulation. Compared to the previous rigid-flexible coupling model where the kinematic chains are all flexible links or where the joints are all flexible components, the inertia matrix and the stiffness matrix are not constant matrix which leading to the differences in respect of dynamic performance in model. To verify the correctness of the derived dynamics equations, the dynamics solutions of the spatial parallel robot from an ideal rigid-body model and the FFR model containing rigid and flexible coordinates were established by an FFR formulation. Furthermore, a finite element analysis (FEA) model, which included rigid links and flexible spatial links, was constructed for comparison. The comparison of the three models showed that the trajectory trends were the same, but the motion trajectories of the end-effector obtained by the FFR and FEA models varied within a certain range, and the maximum variations occurred at the peaks of the trajectories. However, since the FFR model considered the coupling effects of rigid and flexible links and the micro-displacement of the end-effector, the amount of deformation was the largest.

Coupling relationship of the non-ideal parallel mechanism using modified Craig-Bampton method

The coupling relationship in the dynamics model of 4-SPS/PS (P-prismatic joint, S-spherical joint) parallel mechanism with a flexible moving platform and clearance spherical joint is investigated. Two primary coupling relationships are studied: (i) the coupling between reference motion and elastic deformation; (ii) the coupling between the elastic vibration and collision. Firstly, the dynamic model of the flexible moving platform is formulated using the floating frame of reference (FFR) formulation. According to the topology of this parallel mechanism, the fixed-fixed reference conditions are selected and imposed at the finite element (FE) analysis stage for the thin-plate element. Also, considering that the conventional Craig-Bampton (CB) method does not impose any reference condition at FE analysis stage, therefore, a modified CB method is proposed to obtain the fixed-fixed modes, which is validated by normal mode approach. Secondly, the clearance is introduced to one of the spherical joints in the parallel mechanism. The normal and tangential contact forces are calculated based on the Lankarani-Nikravesh contact force model and a modified Coulomb friction model, respectively. In addition, the effect of two coupling relationships on the dynamic response of this parallel mechanism with various thickness of the moving platform is discussed. Finally, the simulation results reveal that the coupling between reference motion and elastic deformation can be ignored in certain situations. However, the coupling between the clearance spherical joint and flexible moving platform deserves more attention, wherein, the flexibility of the moving platform leads to more dramatic collision when its deformation is relatively large, oppositely, it behaves like a dashpot damper to make the system more stable when the deformation is small. This phenomenon also depends on different modal representations.

Development of Geometrically Accurate Continuum-Based Tire Models for Virtual Testing

AbstractIn this paper, an approach based on the integration of computer-aided design and analysis (I-CAD-A) is used to develop new continuum-based finite element (FE) tire models for the small and large deformation analyses. Based on given tire specifications, the mechanics-based geometry/analysis absolute nodal coordinate formulation (ANCF) is used to define the tire geometry with the same degree of accuracy as B-splines and nonuniform rational B-spline (NURBS), widely used in the computer-aided design (CAD) systems. In the case of large deformations, the ANCF geometry can be used directly as the analysis mesh without the need for conversion or adjustments. In order to define the material parameters that characterize the ANCF tire composite structure, a virtual test rig is developed, and the tire calibration process is performed according to the standards defined by the Society of Automotive Engineers (SAE). In order to develop small-deformation models that can be used in the prediction of the tire frequencies and mode shapes, the ANCF position vector gradients are consistently written in terms of rotation parameters, leading to geometrically accurate floating frame of reference (FFR) finite elements, referred to as ANCF/FFR elements. Using this mechanics-based geometry/analysis approach, new geometrically accurate reduced-order tire models are systematically developed and used to define vibration equations for the prediction of the tire frequencies, which are verified using a commercial FE software. The element stiffness matrix is calculated using the general continuum mechanics approach (GCM), and the effectiveness of the strain split method (SSM) for locking alleviation is tested. The results obtained in this investigation show that the I-CAD-A tire modeling approach can be used to develop geometrically accurate tire models suited for the large-deformation multibody system (MBS) problems as well as for the prediction of the tire frequencies and mode shapes.

Floating Frame of Reference formulation for modeling flexible multi-body systems in premise operational conditions

The Floating Frame of Reference (FFR) formulation is a well-established and reliable method for modeling flexible multi-body systems. The FFR formulation has been adopted for dynamic systems that are characterized by large rotations with relatively small deformations. Many scientific papers have pointed out these characteristics with the scrutiny of the simulation results and comparisons with other modeling techniques. However, the FFR is still enclosed in the theoretical aspects and simulation work and faces difficulties when being applied to practical systems. The crucial point in these difficulties centers on coordinate reduction and the associated mapping between nodal and modal coordinates. The process of selecting the necessary modes may be theoretically simple, but the situation is different when applied in a real operational environment. The strategy developed in this work combines the Operational Modal Analysis, specifically the Frequency Domain Decomposition (FDD) approach, and the FFR formulation to build a suitable model of practical multi-body systems. The output model has been validated experimentally. The results show that the proposed FFR-FDD method can be efficiently used to construct multi-body models for those systems that work in premise operational conditions.

Deformation basis and kinematic singularities of constrained systems

This paper demonstrates that arbitrarily introducing deformation degrees of freedom does not always solve the kinematic singularities of over-constrained systems. To address this fundamental problem, this paper proposes different methods that can be used to eliminate the initial-configuration singularity of over-constrained systems when modeled using multibody system formulations such as the general nonlinear finite element floating frame of reference (FFR) formulation. It is shown that the constraint Jacobian matrix of flexible-body models, which are not topologically over-constrained, can be singular. This fundamental problem, encountered in several heavily constrained flexible multibody system applications, such as vehicles, parallel mechanisms, and industrial robots, cannot be solved by automatic elimination of redundant constraints, a feature offered by several commercial multibody system computer programs. Automatic elimination of redundant contraints in systems which are not topologically over-constrained can lead to topological changes, resulting in different solutions with different frequency contents. A simple static-force benchmark problem, with known solution, is used in this paper to shed light on the effect of using different sets of deformation basis vectors, defined using the FFR reference conditions, on the rank of the constraint Jacobian matrix. Three methods for the systematic elimination of the initial-configuration rank deficiency of the constraint Jacobian matrix are proposed. The first method is the modal perturbation method in which selected elements of the modal transformation matrix are perturbed to preserve the system topology and the solution accuracy. The second method defines the deformation basis vectors using the new geometrically accurate absolute nodal coordinate formulation (ANCF)/FFR finite elements. These elements can lead to coupled axial and bending deformation basis vectors, which cannot be obtained using conventional finite elements. In the third method, an equivalent system that has the same solution as the original problem is developed by using a proper set of multibody system constraint equations. The results obtained in this investigation confirm the fact that the choice of the deformation basis vectors should not be restricted to one set, such as the free-free modes, to avoid obtaining incorrect results.

Dynamics investigation of spatial parallel mechanism considering rod flexibility and spherical joint clearance

The dynamic model of 4-SPS/PS parallel mechanism with a flexible actuated rod and clearance spherical joint is established based on the equation of motion. Firstly, the flexible actuated rod is modeled using finite element (FE) 3D beam based on the floating frame of reference (FFR) formulation since small deformation occurs in the rod. In order to build the actual dynamic model, some rigid joints are introduced to connect the related components in 4-SPS/PS parallel mechanism. Secondly, two different sets of reference conditions are imposed at the FE analysis stage for the 3D beam to obtain the free-free modes and fixed-fixed modes based on the normal mode approach, which circumvents the fact that the free-free modes are not suitable for some instances. Further, the dimension of the whole dynamic model is reduced by the normal mode approach as well. Besides, clearance is introduced to one of the spherical joints in this parallel mechanism. The normal and tangential contact forces are estimated based on the Lankarani–Nikravesh contact force model and a modified Coulomb friction model, respectively. Finally, the effects of the free-free modes and fixed-fixed modes from the flexible actuated rod on the dynamic responses of the parallel mechanism with clearance spherical joint are firstly discussed in this investigation. The comparative analysis between considering flexible actuated rod (FAR model), considering clearance spherical joint (CSJ model) and simultaneously considering flexible actuated rod and clearance spherical joint (FAR-CSJ model) has been carried out. The simulation results showed that a reliable and comprehensive solution requires both appropriate reference conditions, and taking the clearance spherical joint and the flexible moving platform into consideration.

Use of mixed coordinates in modeling wind turbines including tubular tower

Abstract. This paper studies the effect of the tower dynamics upon the wind turbine model by using mixed sets of rigid and/or nodal and/or modal coordinates within multibody system dynamics approach. The nodal model exhibits excellent numerical properties, especially in the case where the rotation of the rotor-blade is extremely high, and therefore, the geometric stiffness effect can not be ignored. However, the use of nodal models to describe the flexibility of large multibody systems produces huge size of coordinates and may consume massive computational time in simulation. On the other side, the dynamics of the tower as well as other components of wind turbine remain exhibit small deformations and can be modeled using Cartesian and/or reduced set of modal coordinates. The paper examines a method of using mixed sets of different coordinates in the same model, although there are differences in the scale and the physical interpretation. The equations of motion of the wind-turbine model is presented based on the floating frame of reference formulation. The mixed coordinates vector consists of three sets: Cartesian coordinates set to present the rigid body motion (nacelle and rotor bodies), elastic nodal coordinates for rotating blades, and reduced-order modal coordinates for low speed components and those that deflect by simple motion shapes (circular Tower). Experimental validation has been carried out successfully, and consequently, the proposed model can be utilized for design process, identification and health monitoring aspects.

Integration of geometry and small and large deformation analysis for vehicle modelling: chassis, and airless and pneumatic tyre flexibility

The goal of this study is to propose an approach for developing new and detailed vehicle models that include flexible components with complex geometries, including chassis, and airless and pneumatic tyres with distributed inertia and elasticity. The methodology used is based on integration of geometry, and small and large deformation analysis using a mechanics-based approach. The floating frame of reference (FFR) formulation is used to model the small deformations, whereas the absolute nodal coordinate formulation (ANCF) is used for the large deformation analysis. Both formulations are designed to correctly capture complex geometries including structural discontinuities. To this end, a new ANCF-preprocessing approach based on linear constraints that allows for systematically eliminating dependent variables and reducing the component model dimension is proposed. One of the main contributions of this paper is the development of the first ANCF airless tyre model which is integrated in a three-dimensional multibody system (MBS) algorithm designed for solving the differential/algebraic equations of detailed vehicle models. On the other hand, relatively stiff components with complex geometries, such as the vehicle chassis, are modelled using the finite element (FE) FFR formulation which creates a local linear problem that can be exploited to eliminate high frequency and insignificant deformation modes. Numerical examples that include a simple ANCF pendulum with structural discontinuities and a detailed off-road vehicle model consisting of flexible tyres and chassis are presented. Three different tyre types are considered in this study; a brush-type tyre, a pneumatic FE/ANCF tyre, and an airless FE/ANCF tyre. The numerical results are obtained using the general purpose MBS computer program Systematic Integration of Geometric Modelling and Analysis for the Simulation of Articulated Mechanical Systems (SIGMA/SAMS).

Integration of computer-aided design and analysis: application to multibody vehicle systems

Virtual design and durability investigations are currently performed in automotive industries using three different and incompatible systems: computer-aided design (CAD) system for geometry creation, finite element (FE) software for developing the analysis mesh, and multibody system (MBS) software for automatically generating and numerically solving the differential-algebraic equations (DAE's). This paper proposes a new computer-aided engineering (CAE) approach based on the integration of computer-aided design and analysis (I-CAD-A). The proposed mechanics-based approach achieves seamless geometry/analysis integration, and allows for solid modelling multi-component systems from the outset. The geometrically accurate mechanics-based solid models can be systematically used as the analysis meshes in the small deformation floating frame of reference (FFR) and/or in the large deformation absolute nodal coordinate formulation (ANCF) investigations. In this new approach, ANCF finite elements are used as the basis for creating the geometry for both small and large deformation analyses. In the case of small deformations, ANCF geometry is systematically converted to reduced-order consistent rotation-based formulation (CRBF) FFR mesh, which can be systematically used with standard coordinate reduction techniques to eliminate high-frequency insignificant modes of vibration. The paper discusses the fundamental differences between the proposed method and the isogeometric analysis (IGA) approach and presents illustrative pilot examples to demonstrate the new concepts and the feasibility of developing the mechanics-based design procedure.

Integration of geometry and small and large deformation analysis for vehicle modelling: chassis, and airless and pneumatic tyre flexibility

The goal of this study is to propose an approach for developing new and detailed vehicle models that include flexible components with complex geometries, including chassis, and airless and pneumatic tyres with distributed inertia and elasticity. The methodology used is based on integration of geometry, and small and large deformation analysis using a mechanics-based approach. The floating frame of reference (FFR) formulation is used to model the small deformations, whereas the absolute nodal coordinate formulation (ANCF) is used for the large deformation analysis. Both formulations are designed to correctly capture complex geometries including structural discontinuities. To this end, a new ANCF-preprocessing approach based on linear constraints that allows for systematically eliminating dependent variables and reducing the component model dimension is proposed. One of the main contributions of this paper is the development of the first ANCF airless tyre model which is integrated in a three-dimensional multibody system (MBS) algorithm designed for solving the differential/algebraic equations of detailed vehicle models. On the other hand, relatively stiff components with complex geometries, such as the vehicle chassis, are modelled using the finite element (FE) FFR formulation which creates a local linear problem that can be exploited to eliminate high frequency and insignificant deformation modes. Numerical examples that include a simple ANCF pendulum with structural discontinuities and a detailed off-road vehicle model consisting of flexible tyres and chassis are presented. Three different tyre types are considered in this study; a brush-type tyre, a pneumatic FE/ANCF tyre, and an airless FE/ANCF tyre. The numerical results are obtained using the general purpose MBS computer program Systematic Integration of Geometric Modelling and Analysis for the Simulation of Articulated Mechanical Systems (SIGMA/SAMS).

Integration of computer-aided design and analysis: application to multibody vehicle systems

Virtual design and durability investigations are currently performed in automotive industries using three different and incompatible systems: computer-aided design (CAD) system for geometry creation, finite element (FE) software for developing the analysis mesh, and multibody system (MBS) software for automatically generating and numerically solving the differential-algebraic equations (DAE's). This paper proposes a new computer-aided engineering (CAE) approach based on the integration of computer-aided design and analysis (I-CAD-A). The proposed mechanics-based approach achieves seamless geometry/analysis integration, and allows for solid modelling multi-component systems from the outset. The geometrically accurate mechanics-based solid models can be systematically used as the analysis meshes in the small deformation floating frame of reference (FFR) and/or in the large deformation absolute nodal coordinate formulation (ANCF) investigations. In this new approach, ANCF finite elements are used as the basis for creating the geometry for both small and large deformation analyses. In the case of small deformations, ANCF geometry is systematically converted to reduced-order consistent rotation-based formulation (CRBF) FFR mesh, which can be systematically used with standard coordinate reduction techniques to eliminate high-frequency insignificant modes of vibration. The paper discusses the fundamental differences between the proposed method and the isogeometric analysis (IGA) approach and presents illustrative pilot examples to demonstrate the new concepts and the feasibility of developing the mechanics-based design procedure.

Geometrically accurate infinitesimal-rotation spatial finite elements

In this paper, a general procedure is used to develop new geometrically accurate infinitesimal-rotation finite elements (FE). New spatial beam, plate, and solid elements are developed in terms of constant geometric coefficients obtained using the matrix of position vector gradients. The spatial beam, plate, and solid element shape functions are developed using the displacement field of the absolute nodal coordinate formulation (ANCF). These elements are suited for developing reduced-order models for structural and multibody system (MBS) analyses, particularly when the floating frame of reference (FFR) formulation is used. The initial geometry of the new elements, referred to as the ANCF/FFR, is related to B-splines and NURBS (non-uniform rational B-splines) by a linear mapping, and therefore, their use does not lead to geometry distortion when geometry models are converted to analysis meshes. The main contribution of this technical note is the proposed general procedure for the development of the geometrically accurate spatial ANCF/FFR elements and demonstrating the use of this procedure by developing the ANCF/FFR displacement field of three different spatial elements.