Rigid Body Condition Research Articles

Numerical simulation of flow behavior in basilar bifurcation computed tomography angiography.

In this study, a moving boundary deformation model based on four-dimensional computed tomography angiography (4D-CTA) with high temporal resolution is constructed, and blood flow dynamics of cerebral aneurysms are investigated by numerical simulation. A realistic moving boundary deformation model of a cerebral aneurysm was constructed based on 4D-CTA in each phase. Four hemodynamic factors (wall shear stress [WSS], wall shear stress divergence [WSSD], oscillatory shear index [OSI], and residual residence time [RRT]) were obtained from numerical simulations, and these factors were evaluated in basilar artery aneurysms. Comparison of the rigid body condition and the moving boundary condition investigating the relationship between wall displacement and hemodynamic factors clarified that the spatial-averaged WSS and maximum WSSD considering only the aneurysmal dome has a large difference between conditions during the peak systole, and there were also significant differences in OSI and RRT.

Comparative Study of Two Pose Measuring Systems Used to Reduce Robot Localization Error

The performance of marker-based, six degrees of freedom (6DOF) pose measuring systems is investigated. For instruments in this class, the pose is derived from locations of a few three-dimensional (3D) points. For such configurations to be used, the rigid-body condition—which requires that the distance between any two points must be fixed, regardless of orientation and position of the configuration—must be satisfied. This report introduces metrics that gauge the deviation from the rigid-body condition. The use of these metrics is demonstrated on the problem of reducing robot localization error in assembly applications. Experiments with two different systems used to reduce the localization error of the same industrial robot yielded two conflicting outcomes. The data acquired with one system led to substantial reduction in both position and orientation error of the robot, while the data acquired with a second system led to comparable reduction in the position error only. The difference is attributed to differences between metrics used to characterize the two systems.

Input signal effects on the locomotion of a robotic colonoscope activated by a flexible shaft

Most robotic colonoscopes do not allow sufficient space for high capacity motors since their power sources are equipped in their bodies. Therefore, a robotic colonoscope activated by an external motor through a flexible shaft has been presented. Unfortunately, robot rotations resulting from excessive input torque are observed under some input voltage signals. These rotations occur when the load torque on the flexible shaft exceeds a critical torque value, which is the maximum torque satisfying the rigid body condition. The excessive-torque effect must be eliminated since each rotation causes a velocity reduction as well as twisting of the colon. Therefore, to suppress the rotation by reducing the load torque, the input and load torques are investigated in connection to the input signal. Conclusively, the maximum load torque of the triangular function is the smallest among the input signals and does not exceed the critical torque, which causes the rotation of the robot body. To verify the usefulness of the theoretical and experimental load torque results, in-vitro tests are performed in an acrylic pipe and excised colon for all input functions. As expected with the load torque results according to the input signal, the robot with the triangular function achieves the best performance regardless of experimental environment.

A quaternion-based simulation of multirotor dynamics

The main problem addressed in this paper is the quaternion-based trajectory control of a microcopter consisting of six rotors with three pairs of counter-rotating fixed-pitch blades, known as hexacopter. If the hypothesis of rigid body condition is assumed, the Newton–Euler equations describe the translational and rotational motion of the drone. The standard Euler-angle parametrization of three-dimensional rotations contains singular points in the coordinate space that can cause failure of both dynamical model and control. In order to avoid singularities, all the rotations of the microcopter are thus parametrized in terms of quaternions and an original proportional derivative (PD) regulator is proposed in order to control the dynamical model. Numerical simulations will be performed on symmetrical flight configuration, proving the reliability of the proposed PD control technique.

Influence of the boundary conditions on FE-modeling of longitudinally stiffened I-girders subjected to concentrated loads

Longitudinally stiffened I-girders are commonly used to build incrementally launched steel bridges. During the bridge launching, the girders are subjected to concentrated loading at the support points. These loads are generally larger than those the structure would sustain once located in its final operating position. Numerical studies have considered girder segments subjected to concentrated loading where the boundaries are simulated by kinematic constraints. It represents rigid body conditions where elements at the supported end are allowed only to rotate about an axis perpendicular to the girder web. The load is applied on the girder flange along a small length compared to the total width of the evaluated segment. This paper is aimed at investigating the validity of this hypothesis for longer lengths of the applied load. Herein, the ultimate load of a stiffened girder is determined through finite element modeling, considering the boundaries conditions in two different ways: (1) considering kinematic constraints; and (2) simulating a transverse stiffener. In addition, the used model considers the plastic behavior of the material, the existence of imperfections in the web of the girder and the effects of large deformations. The results show that for short length loadings both hypotheses yield similar results. However, as the loading length increases, significant differences in the results are observed.

Binding Force Analysis of Multiple Pairs of Bars Space RCCR Mechanism without Inertia Force

In close to the rigid body condition,to solve the binding force of multiple pairs of bars space RCCR mechanism,first, starting from solving main binding force of three-pair bars space RCCR mechanism by the theoretical analysis, to have obtained the change law of the main binding force without the inertial force (extremely low speed) by using the computational multibody dynamics software ’COSMOSMotion’ and then summed up the equivalent tangential force through the investigation of the simulation data. Finally the concept of equivalent tangential binding force was expanded to 4, 5, 6 pairs of bars space RCCR mechanism.

Singularity kinematics principle and position-singularity analyses of the 6-3 Stewart-Gough parallel manipulators

This paper presents a new principle and method of kinematics to analyze the singularity of Stewart-Gough parallel manipulators and addresses the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulators for special orientations. Based on the kinematic relationship of a rigid body, a necessary and sufficient condition that three velocities of three non-collinear points in a moving rigid body can determine a screw motion is addressed and some typical singular configurations of the 6-3 Stewart-Gough parallel manipulators are also addressed in detail. With the above-mentioned condition, a symbolic analytical polynomial expression of degree three in the moving platform position parameters, representing the position-singularity locus of the 6-3 Stewart-Gough manipulators for special orientations, is derived; and the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulator for these special orientations is investigated at length. It is shown that position-singularity loci of the 6-3 Stewart-Gough parallel manipulator for these special orientations will be a plane and a hyperbolic paraboloid, even three intersecting planes.

Only a single implanted marker is needed for tracking lung cancers for IGRT

Only a single implanted marker is needed for tracking lung cancers for IGRT

A comparison of four functional methods to determine centers and axes of rotations

Several functional methods to determine joint centers of rotation (CoR) and axes of rotation (AoR) have been reported in the literature. These have previously been compared using noise introduced to marker positions. The current study compares four of these methods under both rigid body and deformable body conditions using a mechanical analog of the lower extremity. In the latter condition, significant inter-marker distance changes were present in patterns directly related to the joint motion. Both hip CoR location and knee AoR location and direction are determined. Results indicate that while all methods produced accurate measures under rigid body conditions (<5 mm location and <2° direction), there were many differences between methods in deformable conditions. Under these conditions, the method described by Gamage and Lasenby performed better than the other methods examined. Maximum mean errors for this technique were approximately 1 cm for CoR and AoR locations and 1° for AoR direction.

Approximation of derivatives in semi-analytical structural optimization

This paper presents a straightforward and generally applicable method for detection and elimination of errors in semi-analytical design sensitivities for any kind of FE-formulation. The basic property of the semi-analytical approach is that derivatives of the stiffness matrix and the load vector are approximated by finite differences. Obviously, truncation errors occur by this method which depend on the chosen step size and the kinematic assumptions of the mechanical model. The accuracy problems in the semi-analytical sensitivity analysis result from these approximation errors [Barthelemy B, Haftka RT. Accuracy analysis of the semi-analytical method for shape sensitivity calculation. Mech Struct Mach 1988;18:407–32]. In this contribution two beam elements (Euler–Bernoulli kinematics, Timoshenko kinematics) are utilized to emphasize the consequences of the approximation errors by an analytical computation of the error terms. These two elements show serious differences in the errors of the sensitivities. The ideas gained by these simple 1-d elements are extended further to 3-d elements with Reissner–Mindlin and Kirchhoff kinematics. The errors of the finite difference approximation of the derivatives may become serious, so it is necessary to correct them to obtain exact sensitivities. There exists a great variety of methods in the literature which try to eliminate the errors in the design sensitivities. Important contributions are published by Haftka and Adelmann, Mlejnek, Cheng and Olhoff, V. Keulen and De Boer among many others. In this paper, a method for the computation of correction factors based on product spaces of rigid body rotation vectors is presented. A straightforward derivation yields to a rigid body condition for the stiffness matrix derivative. The approximation of this derivative violates this rigid body condition due to the changed basis of the perturbed element. By the proposed method one obtains a set of correction factors related to the rigid body rotation vectors of the specific finite element. Due to the modification of the approximated stiffness matrix derivative by this set of factors one finally gets ‘exact’ sensitivities. The improved approximation of the stiffness matrix derivative satisfies the above mentioned rigid body condition. The basic advantage of the proposed method is the efficiency and the independence on the Finite Element formulation. In contrast to many other correction methods published so far, this approach is applicable to all kind of Finite Elements without major modifications. This gives rise to general shape optimization algorithms for a huge amount of finite elements without the necessity to derive each single element analytically.

The immersed boundary-lattice Boltzmann method for solving fluid–particles interaction problems

A new computational method, the immersed boundary-lattice Boltzmann method, is presented. This method is a combination and utilizes the most desirable features of the lattice Boltzmann and the immersed boundary methods. The method uses a regular Eulerian grid for the flow domain and a Lagrangian grid to follow particles that are contained in the flow field. The rigid body conditions for the fluid and the particles are enforced by a penalty method, which assumes that the particle boundary is deformable with a high stiffness constant. The velocity field of the fluid and particles is solved by adding a force density term into the lattice Boltzmann equation. This novel method preserves the advantages of LBM in tracking a group of particles and, at the same time, provides an alternative and better approach to treating the solid–fluid boundary conditions. The method also solves the problems of fluctuation of the forces and velocities on the particles when the “bounce-back” boundary conditions are applied. This method enables one to simulate problems with particle deformation and fluid–structure deformation. Its results are validated by comparison with results from other methods.

Benchmark test cases for evaluation of computer-based methods for detection of setup errors: Realistic digitally reconstructed electronic portal images with known setup errors

Purpose : The purpose of this investigation was to develop methods and software for computing realistic digitally reconstructed electronic portal images with known setup errors for use as benchmark test cases for evaluation and intercomparison of computer-based methods for image matching and detecting setup errors in electronic portal images. Methods and Materials : An existing software tool for computing digitally reconstructed radiographs was modified to compute simulated megavoltage images. An interface was added to allow the user to specify which setup parameter(s) will contain computer-induced random and systematic errors in a reference beam created during virtual simulation. Other software features include options for adding random and structured noise, Gaussian blurring to simulate geometric unsharpness, histogram matching with a “typical” electronic portal image, specifying individual preferences for the appearance of the “gold standard” image, and specifying the number of images generated. The visible male computed tomography data set from the National Library of Medicine was used as the planning image. Results : Digitally reconstructed electronic portal images with known setup errors have been generated and used to evaluate our methods for automatic image matching and error detection. Any number of different sets of test cases can be generated to investigate setup errors involving selected setup parameters and anatomic volumes. This approach has proved to be invaluable for determination of error detection sensitivity under ideal (rigid body) conditions and for guiding further development of image matching and error detection methods. Example images have been successfully exported for similar use at other sites. Conclusions : Because absolute truth is known, digitally reconstructed electronic portal images with known setup errors are well suited for evaluation of computer-aided image matching and error detection methods. High-quality planning images, such as the visible human CT scans from the National Library of Medicine, are essential for producing realistic images. Sets of test cases with systematic and random errors in seelcted setup parameters and anatomic volumes are suitable for use as standard benchmarks by the radiotherapy community. In addition to serving as an aid to research and development, benchmark images may also be useful for evaluation of commercial systems and as part of a quality assurance program for clinical systems. Test cases and software are available upon request.

Vibration Modes and Frequencies of Timoshenko Beams With Attached Rigid Bodies

The equations of motion and boundary conditions for a free-free Timoshenko beam with rigid bodies attached at the endpoints are derived. The natural boundary conditions, for an end that has an attached rigid body, that include the effects of the body mass, first moment of mass, and moment of inertia are included. The frequency equation for a free-free Timoshenko beam with rigid bodies attached at its ends which includes all the effects mentioned above is presented and given in terms of the fundamental frequency equations for Timoshenko beams that have no attached rigid bodies. It is shown how any support / rigid-body condition may be easily obtained by inspection from the reported frequency equation. The mode shapes and the orthogonality condition, which include the contribution of the rigid-body masses, first moments, and moments of inertia, are also developed. Finally, the effect of the first moment of the attached rigid bodies is considered in an illustrative example.

A study of accurate analysis system through the boundary element methods. (1st Report, Introduction of integral equation with relative quantity).

In the usual boundary element method, some special numerical techniques have been developed in order to get accurate solutions at internal points near a boundary where the singularity of the integral equation becomes very strong. However, such superior devices have not succeeded in completely removing the singularity except the analytical integral scheme which tends to contain bigger errors due to discretization. From this point of view, a boundary integral equation i newly formulated. In the implementation, a relative quantity of potential or displacement function is sued. In this report, we confirm the excellence of the present device, and equivalence of the present formulation with relative quantity to the rigid body condition and to the constant potential condition is verified.

Natural coordinates for the computer analysis of multibody systems

In this paper we will describe a new method for the computer kinematic and dynamic analysis of a wide range of three-dimensional mechanisms or multibody systems. This method is based on a new system of non-independent coordinates that use Cartesian coordinates of points and Cartesian components of unitary vectors in order to describe the position and the motion of the system. Angular coordinates are not used. The kinematic constraint equation comes in two ways, from the rigid-body condition for each element and from the joints or kinematic pairs. The consideration of unitary vectors facilitates considerably the formulation of pair constraints when the pair is associated with a particular direction, as is the case with revolute (R), cylindrical (C), or prismatic (P) pairs. The constraint equations are quadratic in the problem coordinates and they never involve transcendental functions. The dynamic differential equations are obtained in a very simple and effective way from the theorem of virtual power. Finally, two examples will be presented.

A triangular thin-shell finite element based on discrete Kirchhoff theory

A three-node, curved thin-shell triangular element with simple nodal connections is developed. The displacement and rotation components are independently interpolated by complete cubic and quadratic polynomials respectively. The Kirchhoff hypothesis is enforced at a discrete number of points in the element. The rigid-body displacement condition is satisfied by isoparametric interpolation of the shell geometry within the element. A detailed numerical evaluation through a number of standard problems is performed.

Correction of rigid body conditions. 3. Correction by indirect observation

Articulator movement and mandibular movement are usually regarded as rigid body movement. When we observe the three-dimensional movement of an articulator to which some targets are fixed, we obtain the co-ordinate (X, Y, Z) of each target in the rectangular coordinate system on a measuring apparatus. As accidental error is contained in each value, any distance between targets, which should be constant, is slightly changed on the observational occasion. Namely, the rigid body condition is not satisfied. The method of least squares is useful to correct accidental errors and give us desirable result of observation as the most provable value.In this article, we investigate to correct accidental errors by means of the indirect observation of the method of least squares. When we correct accidental errors by using this method, we get the position (Xo, Yo, Zo) of the point, which is the translational and rotational center of the articulator, and three rotational angles (Ε, Φ, Ψ) as the most probable value. Using these values, we are able to analyze the movement of any point on the articulator: We can obtain the translation and rotation of teeth on the articulator.

剛体条件の補正に関する研究 ＩＶ 誤差の伝播

剛体条件の補正に関する研究 ＩＶ 誤差の伝播

Comparison of sound scattering by rigid and elastic obstacles in water

Acoustic wave scattering by prolate and oblate spheroids and finite cylinders immersed in water is compared when rigid body and elastic boundary conditions, respectively, are satisfied at the fluid–scatterer interface. The frequency dependence of the scattered farfield is obtained for various angles of incidence for both types of boundary conditions using the null field or T-matrix approach. From our computations it is concluded that only for restricted materials properties of the scatterer, scattering geometry and scatterer shape, the scattering characteristics of an elastic obstacle, and a rigid obstacle of the same shape are comparable up to wavelengths comparable to the size of the obstacle.