Background Computed tomography(CT) and cone-beam computed tomography(CBCT) image registration play pivotal roles in computer-assisted navigation for orthopedic surgery. Traditional methods often apply uniform deformat...Background Computed tomography(CT) and cone-beam computed tomography(CBCT) image registration play pivotal roles in computer-assisted navigation for orthopedic surgery. Traditional methods often apply uniform deformation models, neglecting the biomechanical differences between rigid structures and soft tissues, which compromises registration accuracy, especially during significant bone displacements. Method To address this issue, we introduce RE-Reg, a rigid-elastic CT-CBCT image registration framework that jointly learns rigid bone motion and soft tissue deformation. RE-Reg incorporates a rigid alignment(RA) module to estimate global bone motion and an elastic deformation(ED) module to model soft tissue deformation, preserving bony structures through bone shape preservation(BSP) loss. Result Our comprehensive evaluation on publicly available datasets demonstrates that RE-Reg significantly outperforms existing methods in terms of registration accuracy and rigid bone structure preservation, achieving a 1.3% improvement in Dice similarity coefficient(DSC) and a 23% reduction in rigid bone deformation(%Δvol) compared with the best baseline. Conclusion This framework not only enhances anatomical fidelity but also ensures biomechanical plausibility and provides a valuable tool for image-guided orthopedic surgery. This code is available athttps://github.com/Zq-Huang/RE-Reg.展开更多
In order to realize the small error attitude transformation of a free floating space robot,a new method of three degrees of freedom（ DOF） attitude transformation was proposed for the space robot using a bionic joint...In order to realize the small error attitude transformation of a free floating space robot,a new method of three degrees of freedom（ DOF） attitude transformation was proposed for the space robot using a bionic joint. A general kinematic model of the space robot was established based on the law of linear and angular momentum conservation. A combinational joint model was established combined with bionic joint and closed motion. The attitude transformation of planar,two DOF and three DOF is analyzed and simulated by the model,and it is verified that the feasibility of attitude transformation in three DOF space. Finally,the specific scheme of disturbance elimination in attitude transformation is presented and simulation results are obtained.Therefore,the range of application field of the bionic joint model has been expanded.展开更多
In this paper , the unilaterally constrained motions of a large class of rigid bodiessystems are studied both locally and globally. The main conclusion is that locally,such a system bahaves like a particle in a R...In this paper , the unilaterally constrained motions of a large class of rigid bodiessystems are studied both locally and globally. The main conclusion is that locally,such a system bahaves like a particle in a Riemannian manifold with boundary;globally.under the assumption of energy conservation, the system behaves like a billiards system over a Riemannina manifold with boundary展开更多
Recognizing and reproducing spatiotemporal motions are necessary when analyzing behaviors andmovements during human-robot interaction. Rigid body motion trajectories are proven as compact and informativeclues in chara...Recognizing and reproducing spatiotemporal motions are necessary when analyzing behaviors andmovements during human-robot interaction. Rigid body motion trajectories are proven as compact and informativeclues in characterizing motions. A flexible dual square-root function (DSRF) descriptor for representing rigid bodymotion trajectories, which can offer robustness in the description over raw data, was proposed in our previousstudy. However, this study focuses on exploring the application of the DSRF descriptor for effective backwardmotion reproduction and motion recognition. Specifically, two DSRF-based reproduction methods are initiallyproposed, including the recursive reconstruction and online optimization. New trajectories with novel situationsand contextual information can be reproduced from a single demonstration while preserving the similarities withthe original demonstration. Furthermore, motion recognition based on DSRF descriptor can be achieved byemploying a template matching method. Finally, the experimental results demonstrate the effectiveness of theproposed method for rigid body motion reproduction and recognition.展开更多
A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an a...A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation （BIE） is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem （BVP） of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.展开更多
Rigid ellipsoidal objects(gravels and porphyroclasts)in ductile zone is an important factor to indicate the kinematics and dynamics.Jeffery’s theory(Jeffery G,1922),a quantitative research method,for the rotation oft...Rigid ellipsoidal objects(gravels and porphyroclasts)in ductile zone is an important factor to indicate the kinematics and dynamics.Jeffery’s theory(Jeffery G,1922),a quantitative research method,for the rotation ofthe rigid objects(no deformation)in the Newtonian fluid of the simple deformation field has been widely applied by geologists to the study of fabrics in rocks.The theory展开更多
Let M(2)be the group of rigid motions of the plane.The Fourier transform and the Piancherel formula on M(2)can be explicitly given by the general group representation theory.Using this fact.we establish a kind of unce...Let M(2)be the group of rigid motions of the plane.The Fourier transform and the Piancherel formula on M(2)can be explicitly given by the general group representation theory.Using this fact.we establish a kind of uncertainty principle on M(2).The result can easily be generalized to higher dimensional cases.An application of the result yields an uncertainty principle on the Euclidean spaces obtained by R.S.Strichartz.展开更多
Most computational structural engineers are paying more attention to applying loads rather than to DBCs （Displacement Boundary Conditions） because most static stable mechanical structures are working under already p...Most computational structural engineers are paying more attention to applying loads rather than to DBCs （Displacement Boundary Conditions） because most static stable mechanical structures are working under already prescribed displacement boundary conditions. In all of the computational analysis of solving a system of algebraic equations, such as FEM （Finite Element Method）, three translational and three rotational degrees of freedom （DOF） should be constrained （by applying DBCs） before solving the system of algebraic equation in order to prevent rigid body motions of the analysis results （singular problem）. However, it is very difficult for an inexperienced engineer or designer to apply proper DBCs in the case of thermal stress analysis where no prescribed DBCs or constraints exist, for example in water quenching for heat treatment. Moreover, improper DBCs cause incorrect solutions in thermal stress analysis, such as stress concentration or unreasonable deformation phases. To avoid these problems, we studied a technique which performs the thermal stress analysis without any DBCs; and then removes rigid body motions from the deformation results in a post process step as the need arises. The proposed technique makes it easy to apply DBCs and prevent the error caused by improper DBCs. We proved it was mathematically possible to solve a system of algebraic equations without a step of applying DBCs. We also compared the analysis results with those of a traditional procedure for real castings.展开更多
A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynami...A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynamic model with dynamic stiffening is established via the subsystemmodeling framework. It is clearly elucidated for the first time that,dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beamand the transverse vibration deformation of the beam. The modeling approach in this paper successfully avoids problems which are caused by other popular modeling methods nowadays： the derivation process is too complex by using only one dynamic principle; a clearly theoretical explanation for dynamic stiffening can＇t be provided. First,the continuous dynamic models of the flexible beamand the central rigid body are established via structural dynamics and angular momentumtheory respectively. Then,based on the conclusions of orthogonalization about the normal constrained modes,the finite dimensional dynamic model suitable for controller design is obtained. The numerical simulation validations showthat： dynamic stiffening is successfully incorporated into the dynamic characteristics of the first-order model established in this paper,which can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately,and has a clear modeling mechanism,concise expressions and a good convergence.展开更多
The dynamics of a flexible manipulator is investigated in this paper. From the point of view of dynamic balance, the motion equations of a rotating beam with tip load are established by us ing Hamilton' s principl...The dynamics of a flexible manipulator is investigated in this paper. From the point of view of dynamic balance, the motion equations of a rotating beam with tip load are established by us ing Hamilton' s principle. By taking into account the effects of dynamic stiffening and dynamic softening, the stability of the system is proved by employing Lyapunov' s approach. Furthermore, the method of power series is proposed to find the exact solution of the eigenvalue problem The effects of rotating speed and tip load on the vibration behavior of the flexible manipulator are shown in numerical results.展开更多
In this paper,we compute sub-Riemannian limits of Gaussian curvature for a Euclidean C^(2)-smooth surface in the affine group and the group of rigid motions of the Minkowski plane away from characteristic points and s...In this paper,we compute sub-Riemannian limits of Gaussian curvature for a Euclidean C^(2)-smooth surface in the affine group and the group of rigid motions of the Minkowski plane away from characteristic points and signed geodesic curvature for Euclidean C^(2)-smooth curves on surfaces.We get Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane.展开更多
An alternative set of angles for determining the position of a rigid body,instead of Euler angles,is proposed.These angles were used to model the motion of a rigid body(rotor)rotating around a horizontal axis.For the ...An alternative set of angles for determining the position of a rigid body,instead of Euler angles,is proposed.These angles were used to model the motion of a rigid body(rotor)rotating around a horizontal axis.For the proposed angles,equations similar to Euler’s kinematic equations were derived.Most machines with rotating shafts are designed horizontally,and the proposed angles are convenient for studying these machines using Euler’s dynamic equations.Equations were derived that allow one to obtain Euler angles from known proposed angles and to obtain proposed angles from known Euler angles.For a freely rotating rigid body,one can observe the Dzhanibekov’s effect,which can be classified as the periodic motion of an asymmetrical top and a type of tennis racket effect.The horizontal movement of the rotor,which is accompanied by the Dzhanibekov effect,well illustrates the advantages of the proposed angles.Based on Euler’s equations and using the proposed angles,two types of systems of differential equations were obtained.These systems do not degenerate,are tested on a well-known classical example and are applicable to any motion of a rigid body.Systems of differential equations were solved numerically using the Matlab software package using the ode45 subroutine(the simplest solver).The resulting solutions are stable and repeatable.The numerical results obtained are compared with the results obtained using the well-known modified predictor-corrector method.The preference of using the proposed coordinate system for numerical solutions of a system of differential equations compared to Eulerian angles is shown.For the free movement of an asymmetrical top,an analytical solution is known,obtained in the form of elliptic functions.This solution is extended to the Dzhanibekov’s effect and the results obtained are compared with the results of the numerical simulation of the Dzhanibekov’s effect.The formulas were obtained to determine the time before the first 180degree turn and the time between the next 180-degree turns.The formula for determining the time to the first turn was adjusted for the case of non-zero initial conditions for the three angular velocities,taking into account their sign.The known formula for the period of an asymmetrical top movement process during Dzhanibekov’s effect was confirmed.展开更多
Automatic localization,aligning the measured points with the design model,is a basic task in free-form surface inspection.The main difficulty of current localization algorithms is how to define effective distance func...Automatic localization,aligning the measured points with the design model,is a basic task in free-form surface inspection.The main difficulty of current localization algorithms is how to define effective distance function and localization reliability index.This paper proposes a new method of calculating motion parameters and evaluating localization reliability.First,improved modified coefficient is defined and applied to weighted-iteration distance function,which better approximates the point-to-surface closest distance.It can control the contribution ratios of different measured points by considering the curvature feature and iterative residual.Second,the mapping relationship between localization error and geometric error is analyzed,from which a Lyapunov-test statistic is derived to define a frame-independence index.Then,the determination of localization reliability changes into a supposition examination problem.This can avoid rejecting correct motion parameters,which exists in the traditional judgment of absolute root-mean-square distance.In addition,two test experiments are implemented to demonstrate the proposed localization algorithm.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.62025104,62331005,and U22A2052)the Beijing Natural Science Foundation(Grant No.L242100).
文摘Background Computed tomography(CT) and cone-beam computed tomography(CBCT) image registration play pivotal roles in computer-assisted navigation for orthopedic surgery. Traditional methods often apply uniform deformation models, neglecting the biomechanical differences between rigid structures and soft tissues, which compromises registration accuracy, especially during significant bone displacements. Method To address this issue, we introduce RE-Reg, a rigid-elastic CT-CBCT image registration framework that jointly learns rigid bone motion and soft tissue deformation. RE-Reg incorporates a rigid alignment(RA) module to estimate global bone motion and an elastic deformation(ED) module to model soft tissue deformation, preserving bony structures through bone shape preservation(BSP) loss. Result Our comprehensive evaluation on publicly available datasets demonstrates that RE-Reg significantly outperforms existing methods in terms of registration accuracy and rigid bone structure preservation, achieving a 1.3% improvement in Dice similarity coefficient(DSC) and a 23% reduction in rigid bone deformation(%Δvol) compared with the best baseline. Conclusion This framework not only enhances anatomical fidelity but also ensures biomechanical plausibility and provides a valuable tool for image-guided orthopedic surgery. This code is available athttps://github.com/Zq-Huang/RE-Reg.
文摘In order to realize the small error attitude transformation of a free floating space robot,a new method of three degrees of freedom（ DOF） attitude transformation was proposed for the space robot using a bionic joint. A general kinematic model of the space robot was established based on the law of linear and angular momentum conservation. A combinational joint model was established combined with bionic joint and closed motion. The attitude transformation of planar,two DOF and three DOF is analyzed and simulated by the model,and it is verified that the feasibility of attitude transformation in three DOF space. Finally,the specific scheme of disturbance elimination in attitude transformation is presented and simulation results are obtained.Therefore,the range of application field of the bionic joint model has been expanded.
文摘In this paper , the unilaterally constrained motions of a large class of rigid bodiessystems are studied both locally and globally. The main conclusion is that locally,such a system bahaves like a particle in a Riemannian manifold with boundary;globally.under the assumption of energy conservation, the system behaves like a billiards system over a Riemannina manifold with boundary
基金the Science and Technology Commission of Shanghai Municipality(No.20DZ2220400)the Interdisciplinary Program of Shanghai Jiao Tong University(No.YG2021QN117)。
文摘Recognizing and reproducing spatiotemporal motions are necessary when analyzing behaviors andmovements during human-robot interaction. Rigid body motion trajectories are proven as compact and informativeclues in characterizing motions. A flexible dual square-root function (DSRF) descriptor for representing rigid bodymotion trajectories, which can offer robustness in the description over raw data, was proposed in our previousstudy. However, this study focuses on exploring the application of the DSRF descriptor for effective backwardmotion reproduction and motion recognition. Specifically, two DSRF-based reproduction methods are initiallyproposed, including the recursive reconstruction and online optimization. New trajectories with novel situationsand contextual information can be reproduced from a single demonstration while preserving the similarities withthe original demonstration. Furthermore, motion recognition based on DSRF descriptor can be achieved byemploying a template matching method. Finally, the experimental results demonstrate the effectiveness of theproposed method for rigid body motion reproduction and recognition.
文摘A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation （BIE） is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem （BVP） of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.
文摘Rigid ellipsoidal objects(gravels and porphyroclasts)in ductile zone is an important factor to indicate the kinematics and dynamics.Jeffery’s theory(Jeffery G,1922),a quantitative research method,for the rotation ofthe rigid objects(no deformation)in the Newtonian fluid of the simple deformation field has been widely applied by geologists to the study of fabrics in rocks.The theory
文摘Let M(2)be the group of rigid motions of the plane.The Fourier transform and the Piancherel formula on M(2)can be explicitly given by the general group representation theory.Using this fact.we establish a kind of uncertainty principle on M(2).The result can easily be generalized to higher dimensional cases.An application of the result yields an uncertainty principle on the Euclidean spaces obtained by R.S.Strichartz.
文摘Most computational structural engineers are paying more attention to applying loads rather than to DBCs （Displacement Boundary Conditions） because most static stable mechanical structures are working under already prescribed displacement boundary conditions. In all of the computational analysis of solving a system of algebraic equations, such as FEM （Finite Element Method）, three translational and three rotational degrees of freedom （DOF） should be constrained （by applying DBCs） before solving the system of algebraic equation in order to prevent rigid body motions of the analysis results （singular problem）. However, it is very difficult for an inexperienced engineer or designer to apply proper DBCs in the case of thermal stress analysis where no prescribed DBCs or constraints exist, for example in water quenching for heat treatment. Moreover, improper DBCs cause incorrect solutions in thermal stress analysis, such as stress concentration or unreasonable deformation phases. To avoid these problems, we studied a technique which performs the thermal stress analysis without any DBCs; and then removes rigid body motions from the deformation results in a post process step as the need arises. The proposed technique makes it easy to apply DBCs and prevent the error caused by improper DBCs. We proved it was mathematically possible to solve a system of algebraic equations without a step of applying DBCs. We also compared the analysis results with those of a traditional procedure for real castings.
文摘A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynamic model with dynamic stiffening is established via the subsystemmodeling framework. It is clearly elucidated for the first time that,dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beamand the transverse vibration deformation of the beam. The modeling approach in this paper successfully avoids problems which are caused by other popular modeling methods nowadays： the derivation process is too complex by using only one dynamic principle; a clearly theoretical explanation for dynamic stiffening can＇t be provided. First,the continuous dynamic models of the flexible beamand the central rigid body are established via structural dynamics and angular momentumtheory respectively. Then,based on the conclusions of orthogonalization about the normal constrained modes,the finite dimensional dynamic model suitable for controller design is obtained. The numerical simulation validations showthat： dynamic stiffening is successfully incorporated into the dynamic characteristics of the first-order model established in this paper,which can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately,and has a clear modeling mechanism,concise expressions and a good convergence.
文摘The dynamics of a flexible manipulator is investigated in this paper. From the point of view of dynamic balance, the motion equations of a rotating beam with tip load are established by us ing Hamilton' s principle. By taking into account the effects of dynamic stiffening and dynamic softening, the stability of the system is proved by employing Lyapunov' s approach. Furthermore, the method of power series is proposed to find the exact solution of the eigenvalue problem The effects of rotating speed and tip load on the vibration behavior of the flexible manipulator are shown in numerical results.
基金supported by National Natural Science Foundation of China(Grant No.11771070)。
文摘In this paper,we compute sub-Riemannian limits of Gaussian curvature for a Euclidean C^(2)-smooth surface in the affine group and the group of rigid motions of the Minkowski plane away from characteristic points and signed geodesic curvature for Euclidean C^(2)-smooth curves on surfaces.We get Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane.
文摘An alternative set of angles for determining the position of a rigid body,instead of Euler angles,is proposed.These angles were used to model the motion of a rigid body(rotor)rotating around a horizontal axis.For the proposed angles,equations similar to Euler’s kinematic equations were derived.Most machines with rotating shafts are designed horizontally,and the proposed angles are convenient for studying these machines using Euler’s dynamic equations.Equations were derived that allow one to obtain Euler angles from known proposed angles and to obtain proposed angles from known Euler angles.For a freely rotating rigid body,one can observe the Dzhanibekov’s effect,which can be classified as the periodic motion of an asymmetrical top and a type of tennis racket effect.The horizontal movement of the rotor,which is accompanied by the Dzhanibekov effect,well illustrates the advantages of the proposed angles.Based on Euler’s equations and using the proposed angles,two types of systems of differential equations were obtained.These systems do not degenerate,are tested on a well-known classical example and are applicable to any motion of a rigid body.Systems of differential equations were solved numerically using the Matlab software package using the ode45 subroutine(the simplest solver).The resulting solutions are stable and repeatable.The numerical results obtained are compared with the results obtained using the well-known modified predictor-corrector method.The preference of using the proposed coordinate system for numerical solutions of a system of differential equations compared to Eulerian angles is shown.For the free movement of an asymmetrical top,an analytical solution is known,obtained in the form of elliptic functions.This solution is extended to the Dzhanibekov’s effect and the results obtained are compared with the results of the numerical simulation of the Dzhanibekov’s effect.The formulas were obtained to determine the time before the first 180degree turn and the time between the next 180-degree turns.The formula for determining the time to the first turn was adjusted for the case of non-zero initial conditions for the three angular velocities,taking into account their sign.The known formula for the period of an asymmetrical top movement process during Dzhanibekov’s effect was confirmed.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50835004 and 51105155)the China Postdoctoral Science Foundation (Grant No. 20110491145)
文摘Automatic localization,aligning the measured points with the design model,is a basic task in free-form surface inspection.The main difficulty of current localization algorithms is how to define effective distance function and localization reliability index.This paper proposes a new method of calculating motion parameters and evaluating localization reliability.First,improved modified coefficient is defined and applied to weighted-iteration distance function,which better approximates the point-to-surface closest distance.It can control the contribution ratios of different measured points by considering the curvature feature and iterative residual.Second,the mapping relationship between localization error and geometric error is analyzed,from which a Lyapunov-test statistic is derived to define a frame-independence index.Then,the determination of localization reliability changes into a supposition examination problem.This can avoid rejecting correct motion parameters,which exists in the traditional judgment of absolute root-mean-square distance.In addition,two test experiments are implemented to demonstrate the proposed localization algorithm.
