Rotational DOF Research Articles

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 2: shells

Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715---732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples.

2P1-B08 小児外科手術支援のための多自由度持針器の開発(医療ロボティクス・メカトロニクス)

In this paper, we developed multi-DOF forceps for pediatric laparoscopic surgery. Pediatric laparoscopic surgery has many advantages for patents, but it is difficult for surgeons to perform. The motion of the instruments is restricted by the insertion points, and the workspace of children is smaller than that of adults. Therefore, we have proposed and implemented a three-DOF and 3.5-mm-diameter needle driver for pediatric laparoscopic surgery. The grasping DOF of developed needle driver is piston type and actuated by wire. The deflection and rotation DOF are actuated by bevel gears. We checked the range of the deflection and rotation DOF and the grasping power. The experimental results showed that the developed needle driver fulfills all the requirements. Suturing experiment also implied that suturing tasks can be performed.

2P2-Q12 複数のエアジェットによる物体の非接触操作 : 平面3自由度制御方式(インフォマティブ・モーションとモーション・メディア-ロボットの身体性と運動-)

We have proposed a technology for manipulating the position and orientation of an object in a contactless manner using multiple air jets. By regulating the air jet directions and flow rates, the object can be actively "force closured" and its position and orientation can be manipulated freely. In this paper, we report an experimental system with 3 DOF (2 translational DOF and 1 rotational DOF) using four air jets on a planar surface.

Moving Character Analysis of a Novel 3-DOF Parallel Mechanism

A novel 2-TPR/1-SPR spatial 3-DOF parallel mechanism is studied. The studied mechanism is composed of a moving platform connected to a fixed platform by means of three actuated limbs. The two of the three limbs are TPR serial manipulators and the other one is SPR serial manipulator. Each TPR limb consists of a Hoke joint T connecting to the fixed platform, a prismatic pair P, and a revolute pair R connecting to the moving platform. The SPR limb consists of a spherical pair S connecting to the fixed platform, a prismatic pair P, and revolute pair R connecting to the moving platform. Moving character of this mechanism are analyzed by using the theory of screws. The moving platform of this mechanism has one translational DOF, and it is translational moving along the normal direction of the plane which passes through the moving platform. The moving platform of this mechanism also have two rotational DOFs, and they are rotational moving that are rotated the lines which intersect each one of three binding line-vectors of the mechanism at the same time.

OctoMag: An Electromagnetic System for 5-DOF Wireless Micromanipulation

We demonstrate five-degree-of-freedom (5-DOF) wireless magnetic control of a fully untethered microrobot (3-DOF position and 2-DOF pointing orientation). The microrobot can move through a large workspace and is completely unrestrained in the rotation DOF. We accomplish this level of wireless control with an electromagnetic system that we call OctoMag. OctoMag's unique abilities are due to its utilization of complex nonuniform magnetic fields, which capitalizes on a linear representation of the coupled field contributions of multiple soft-magnetic-core electromagnets acting in concert. OctoMag was primarily designed to control intraocular microrobots for delicate retinal procedures, but it also has potential uses in other medical applications or micromanipulation under an optical microscope.

Multi-body dynamics simulation of geometrically exact Cosserat rods

In this paper, we present a viscoelastic rod model that is suitable for fast and accurate dynamic simulations. It is based on Cosserat’s geometrically exact theory of rods and is able to represent extension, shearing (‘stiff’ dof), bending and torsion (‘soft’ dof). For inner dissipation, a consistent damping potential proposed by Antman is chosen. We parametrise the rotational dof by unit quaternions and directly use the quaternionic evolution differential equation for the discretisation of the Cosserat rod curvature.

Dynamic performance comparison and counterweight optimization of two 3-DOF parallel manipulators for a new hybrid machine tool

The dynamic performance of two 3-DOF parallel manipulators, the HALF and the HALF ⋆ , is compared and a new optimization method for the counterweight masses is proposed for the development of a new hybrid machine tool. Since the manipulators have the same mobility of two translational and one rotational DOFs and the machine tool is designed for high-speed machining, it becomes significant to determine which manipulator has better dynamic characteristics. For this purpose, the dynamic models of the manipulators are derived via the Lagrangian formulation and the translational and rotational quantities are separated due to the unit inhomogeneity. Performance indices are proposed to measure the acceleration, velocity, and external loading capabilities, and then are used in counterweight optimization to minimize the actuator forces for the required acceleration and velocity limitations. Simulation results show that the HALF ⋆ provides better linear acceleration and linear velocity performance than the HALF, thus it is chosen for the hybrid machine tool. With the counterweight optimization, the actuator forces for the required maximum accelerations and velocities can be reduced by ten percent

Fully Coupled 10-Degree-of-Freedom Beam Theory for Piecewise Straight Thin-Walled Beams with General Quadrilateral Cross Sections

A fully coupled 10-degree-of-freedom (DOF) beam theory is developed for the analysis of thin-walled closed piecewise straight beams of general quadrilateral cross sections. The developed beam theory can predict the structural response of arbitrarily shaped thin-walled quadrilateral sectioned beams that are curved or connected to each other through a number of angled joints. For accurate prediction, the local effects by four beam sectional deformations such as torsional warping, torsional distortion, bending warping, and bending distortion must be taken into account in addition to the structural responses by standard six translational and rotational DOFs of the Timoshenko beam theory. When two straight beams of general quadrilateral sections meet at an angle, all 10 DOF deformations become fully coupled. Furthermore, it is not easy to derive the exact interface conditions at the angled joint because 10 DOFs have different physical behavior. For the analysis of the beam system in consideration, the section deformation patterns corresponding to all of the 10 DOFs are presented. In particular, the cross-sectional shape functions for bending distortion and bending warping for general quadrilateral sections are derived for the first time. Then, a systematic method to match 10 DOFs of two straight quadrilateral beams meeting at a joint of an arbitrary angle is developed. Several numerical case studies are considered to check the validity of the developed beam analysis.

Singularity Analysis of the H4 Parallel Mechanisms with Isomorphic Sub-chains

H4 mechanism corresponds to a group of parallel mechanisms with good dynamical character,the center components of their movable platforms have three translational DOFs and one rotational DOF. In this group of mechanisms there are four isomorphic sub-chain mechanisms,each sub-chain includes one (S-S)2 quadrilateral bar-suit,and the difference of these four mechanisms is in that their actuated joints or the sub-chains' deployment between base and movable platforms are different. Based on the structure analysis of isomorphic sub-chain mechanisms,the force equilibrium equations of movable platform and sub-chain are established,and force Jacobian matrix are obtained. On which the singularities of the four mechanisms are analyzed by using line geometry method,the discriminating conditions of sub-chain singularity,platform singularity and actuator singularity are proposed,and the kinematic characters of mechanisms at singularity configurations are analyzed. Finally,the configuration examples of an isomorphic sub-chain parallel mechanism in the states of sub-chain singularity,platform singularity and actuator singularity are illustrated.

CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations Part II: Description of the Numerical Tool and Its Outputs

Analytical relationships are given for calculating in a planetary application the radial and orbital roller centrifugal forces usually taken by the outer race and cage-bridge, respectively. Each roller is described using two rotational degrees of freedom (dof), and the cage is described using two radial dof and one rotational dof. The model has been incorporated in a new tool, called CAGEDYN. Many graphical outputs are shown using one example: a needle roller bearing calculated at one given load and speed in a planetary and nonplanetary application with the significant differences outlined. This tool is particularly useful for design and application engineers expecting an answer within a few minutes of CPU time on a standard laptop.

T‐spline finite element method for the analysis of shell structures

AbstractA T‐spline surface is a nonuniform rational B‐spline (NURBS) surface with T‐junctions, and is defined by a control grid called T‐mesh. The T‐mesh is similar to a NURBS control mesh except that in a T‐mesh, a row or column of control points is allowed to terminate in the inner parametric space. This property of T‐splines makes local refinement possible. In the present study, shell formulation based on the T‐spline finite element method (FEM) is presented. Shell formulation based on NURBS or T‐splines has fundamental limitations because rotational DOFs, which are necessary in the shell formulation, cannot be defined on control points. In this study, the simple mapping scheme, in which every control point is mapped into one geometric point on the surface, is employed to eliminate the limitations. Using this mapping scheme, T‐spline FEM can be easily extended to the analysis of shells. The proposed shell formulation is verified through various benchmarking problems. This study is a part of the efforts by the authors for the integration of CAD–CAE processes. Copyright © 2009 John Wiley & Sons, Ltd.

A new family of spatial 3-DOF parallel manipulators with two translational and one rotational DOFs

SUMMARYThis paper proposes a new family of spatial 3-DOF (degree of freedom) parallel manipulators with two translational and one rotational DOFs. The manipulators in this family are the variations of the parallel manipulators, which are capable of very high rotational capability, introduced by X.-J. Liu, J. Wang, and G. Pritschow (“A new family of spatial 3-DoF fully parallel manipulators with high rotational capability,” Mech. Mach. Theory40(4), 475–494, 2005). However, compared with those old manipulators, the new parallel manipulators proposed here have the advantages of simpler kinematics and structure, easier manufacturing, and energy saving.

Ground testing, with a four mass torsion pendulum facility, of an optical-read-out for the LISA gravitational reference sensor

In the last few years the Lisa group in Napoli has developed an Optical Read-Out (ORO) system based on optical levers as an auxiliary and backup readout for the Gravitational Reference Sensor (GRS) of LISA. Bench-top measurements, with a rigid set-up have successfully proven that the ORO fits the requirements for sensitivity both in translational and rotational DOFs, exceeding the capacitive sensor performance in a wide range of frequencies. Last year an ORO system designed in Napoli in collaboration with the Trento LISA group, has been installed, as an auxiliary readout system, on the four mass torsion pendulum developed in Trento. In this paper we report on the testing of this ORO device and its performances in comparison with the capacitive one; we also outline further improvements and their advantages for the torsion pendulum facility performances.

Haptic Wrists: An Alternative Design Strategy Based on User Perception

A new three degree-of-freedom (3DOF) torque feedback wrist is being developed to be added to an existing 3DOF force feedback haptic device. It is difficult to find a satisfactory solution to the mechanical design problem, mainly because of the required large rotational workspace and severe weight constraints. This work proposes an alternative design strategy based on user perception, which allows simplification of the mechanics. The proposed approach consists of substituting the last rotational DOF of the wrist with a pseudohaptic DOF. Thanks to specially designed visuotactile cues, the pseudohaptic DOF is integrated with the active DOF into the same device, being able to generate free motion and collision detection perception to the user. This approach provides for simpler kinematics, lightweight designs, lower inertias, and less friction, which are key advantages for the inclusion of torque feedback into force feedback devices.

Dynamic model and force control of the redundantly actuated parallel manipulator of a 5-DOF hybrid machine tool

SUMMARYThis paper deals with the dynamic model and force control of the redundantly actuated parallel manipulator of a 5-DOF hybrid machine tool. The inverse dynamic model is derived by using the Newton–Euler method. The driving force is optimized by the least-square method. Based on the kinematic and dynamic models, the redundant chain is controlled by force mode and other chains by position mode. The redundantly actuated parallel manipulator is incorporated into a 5-DOF hybrid machine tool which also includes a worktable with a translational DOF and a rotational DOF. The experiments wherein the machine moves along a straight-line trajectory and a circular trajectory show that the machine has a good contouring performance.

Motion pattern analysis of parallel kinematic machines: A case study

This paper looks at the “five-axis machines” for machining operations. These machines have five (or six at maximum) degrees of freedom (dof). The output motion must have at least three translational and two rotational dof. This output motion pattern can be obtained with different structural topologies: serial, parallel, hybrid and with serial and/or parallel manipulators working in co-operation. The latter allows higher motion ranges in rotational and translational dof. Moreover, it provides a good stiffness, a highly valued requisite in applications like machining. Manipulators of this type are characterized by their kinematics to be integrated in the CNC, which requires the study of the relative motion between their modules. This motion is usually complex, and in certain cases presents kinematic relations not evident. This work presents a methodology to solve the motion pattern out of the direct and inverse kinematics of the relative motion between the modules of which the manipulator is composed. On the one hand, the spindle is mounted on a parallel module. On the other hand, the working table is mounted on a serial module. This methodology was applied to the Hermes parallel manipulator in combination with rotary and linear tables. As a result, a series of considerations regarding other possible combinations between modules was made and a new machine is proposed.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods

Discretization of a Continuous Curve

We consider the problem of approximating a finite-length continuous curve by a piecewise linear one whose segments are assumed to be connected by 2 DOF joints. We solve the problem under the assumption that the endpoints of the line segments lie on the continuous curve. Analytical expressions for the relative orientations of each pair of line segments as a function of a single rotational DOF are found. This angle can be chosen arbitrarily or used to optimize a secondary task. The motivating application for this paper is the control of a snake-like robot using gaits designed from shape primitives.

A Refined Double-row Spherical Roller Bearing Model and its Application in Performance Assessment of Moving Race Shaft Misalignments

Largely due to their self-aligning and superior loading capabilities, spherical roller bearings have seen extensive application. Compared with the single-row deep-grooved-ball (DGB) bearing, the dynamics involved in the operation of double-row spherical roller bearings (SRBs) are much more complicated; double-row SRBs have at least twice as many degrees of freedom (DoFs) as DGBs. Also, the contact forces between each one of a pair of rollers and the inner race/outer race can be different, resulting in unbalanced axial forces on the moving race and causing axial displacement and angular movements of the moving race. Due to its complexity, modeling efforts carried out so far have not included the effects of the rotational DoFs of the moving race. Aiming at improving the state of the art, a comprehensive dynamic model of SRBs is developed in this investigation. This model takes into account all the DoFs of the moving race, including the angular movements about both the vertical and horizontal axes. Subsequently, the contact angle between each individual roller and the moving race is correlated with each linear and rotational DoF of the moving race. The model developed in this investigation can quantitatively analyze the effects of linear and rotational shaft misalignments. Therefore, it provides guidelines for optimizing system installation requirements/procedure, which will be valuable for high-precision machine systems. The simulation results demonstrate that the rotational DoFs of the moving race have major effects on the force/displacement responses and thus should be included in the model for a more accurate assessment of the system performance. Extensive case studies are carried out to assess the effects of the loading conditions and radial clearance, as well as shaft misalignment.

Fabric drape simulation by solid-shell finite element method

In the last decade, considerable effort has been channeled into the development of solid-shell finite element models in which there are only translational but no rotational nodal dofs. Comparing with other shell elements, a distinctive advantage of solid-shell elements is that the complication on handling finite rotations does not exist. On the other hand, fabric drape is a typical geometric nonlinear problem in which the problem domain undergoes large displacement and rotation. To date, computational models for drape simulation are mainly grid-based and fe-based. The former models are probably more successful and examples with extensive folds have seldom been reported by using the latter models. In this paper, a bilinear stress-resultant solid-shell element with assumed natural transverse shear and thickness strains is employed for drape analyses. To reduce the computational burden of interpolating the assumed strain field, the solid-shell element is partitioned into a surface, four line and four point sub-elements. The partitioned element is compared with the original elements by popular geometric nonlinear benchmark problems of shells, no practical difference can be noted in both the converged solution and the convergent rate. However, when the elements are applied to drape analyses with long free-hanging length, some nodal directors are often reversed and, thus, the converged solutions are non-physical. The cause has been traced and remedy is devised. Lastly, a number of drape problems with large free-hanging lengths, extensive folds and fabric-to-solid contact are successfully attempted. The predicted views appear to be natural and pleasant.