AN UNCERTAINTY PRINCIPLE ON THE GROUP OF RIGID MOTIONS OF THE PLANE

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.

Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane

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.

ON UNILATERALLY CONSTRAINED MOTIONS OF RIGID BODIES SYSTEMS

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

Amended influence matrix method for removal of rigid motion in the interior BVP for plane elasticity

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.

Introduction of Simulating the Motion of Rigid Ellipsoidal Objects in Ductile Shear Zone Based on the Jeffery's Theory

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

Effects of displacement boundary conditions on thermal deformation in thermal stress problems

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.

Dynamic modeling and simulation for the flexible spacecraft with dynamic stiffening

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.

Bionic Attitude Transformation Combined with Closed Motion for a Free Floating Space Robot

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.

On Flexible Trajectory Description for Effective Rigid Body Motion Reproduction and Recognition

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.

DYNAMICS OF A ROTATING FLEXIBLE MANIPULATOR WITH TIP LOAD

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.

Two Step Forging Process of Spur Gear Based on Rigid Parallel Motion

To improve the forging process of spur gear,the metal flow rule is investigated in detail,and a hypothesis of radial rigid-parallel-motive (RPM) flow mode is given. Based on the RPM mode a novel specific gear forging technology is put forward by introduced upend forging process and constrained divided-flow technique. Firstly,finite element method is used to simulate the upend forging pre-forming and RPM finish forging,and equivalent stress field and load-stroke curve are investigated. Secondly,a corresponding experiment is carried out with pure lead to validate the numerical simulation. Thirdly,the peak value of conventional forging process is also simulated and is used to compare with the novel forging process,and the result shows that the forming force decreases significantly,about 35%. Finally,the effect on forming load of two key process parameters (the height of gear tooth after pre-forming and friction factor) is analyzed,and the superiority of the novel forging process is further proved.

Automatic surface localization by defining weighted-iteration distance function and Lyapunov-test statistic

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.