Acceleration and singularity analyses of a parallel manipulator with a particular topology

In this work, two essential steps, the kinematics and the singularity analysis, dealing with the design process of a parallel manipulator are investigated by means of the theory of screws. The proposed mechanism for the analysis is a parallel manipulator with three degrees of freedom. A simple and compact expression is derived here for the computation of the reduced acceleration state of the moving platform, w.r.t. the fixed platform, by taking advantage of the properties of reciprocal screws, via the Klein form of the Lie algebra e(3). To this end, the reduced acceleration state of the moving platform is written in screw form through each one of the three actuator limbs of the manipulator. Afterwards, the acceleration analysis is completed by taking into proper account the decoupled motion of the parallel manipulator. Of course, as an intermediate step this contribution also provides the velocity analysis of the parallel manipulator. The expressions obtained via screw theory are compact and can be easily translated into computer codes. A numerical example is provided to demonstrate the efficacy of screw theory to efficiently analyze the kinematics of the chosen parallel manipulator. Finally, the numerical results from the kinematic analysis are compared with results produced with a commercially available dynamic and kinematic simulation program.     

NONLINEAR ANALYSIS OF DYNAMIC STABILITY FOR LAMINATED CIRCULAR CYLINDRICAL THICK SHELLS WITH ENDS ELASTICALLY SUPPORTED AGAINST ROTATION

Based on Timoshenko-Mindlin kinematic hypotheses and Hamilton'sprinciple,a dynamic non-linear theory for general laminated circular cylindrical shellswith transverse shear deformation is developed.A multi-mode solution for periodic in-plane loads is formulated for the non-linear dynamic stability of an anti-symmetricangle-ply cylinder with its ends elastically restrained against rotation.The resultedequations in terms of time function are solved by the incremental harmonic balancemethod.     

General Reduced Forms of Constitutive Relations in the Classical Continuum Mechanics

A theory of constitutive relations describing the resistance of bodies to deformation is developed. This theory takes into account the presence of internal body forces and internal kinematic constraints. A number of axioms and a general reduced form of constitutive relations for classical media are proposed. For simple bodies it is proved that the Il'yushin and Noll constitutive relations are equivalent.     

The Kinematics and the Full Minimal Dynamic Model of a 6-DOF Parallel Robot Manipulator

In this paper we present a particular architecture of parallel robots which has six-degrees-of-freedom (6-DOF) with only three limbs. The particular properties of the geometric and kinematic models with respect to that of a classical parallel robot are presented. We show that inverse problems have an analytical solution. However, to solve the direct problems, an efficient numerical procedure which needs to inverse only a 3 × 3 passive Jacobian matrix is proposed. In a second step, dynamic equations are derived using the Lagrangian formalism where the joint variables are passive and active joint coordinates. Based on the geometrical properties of the robot, the equations of motion are derived in terms of only nine coordinates related by three kinematic constraints instead of 18 joint coordinates. The computational cost of the dynamic model obtained is reduced by using a minimum set of base inertial parameters.     

粘性介质上的悬臂梁在冲击载荷作用下的刚塑性动力响应

本文考虑了一个放置在粘性介质上的刚-理想塑性悬臂梁在自由端受冲击载荷时的小变形动力响应。具体讨论了线性粘性介质时矩形脉冲,线性衰减脉冲及瞬时冲击等加载情况,并与无介质解进行了比较,讨论了介质对梁的运动变形模式、最终挠度、能量吸性的影响。     

Shakedown reduced kinematic formulation,separated collapse modes,and numerical implementation

Our shakedown reduced kinematic formulation is developed to solve some typical plane stress problems, using finite element method. Whenever the comparisons are available, our results agree with the available ones in the literature. The advantage of our approach is its simplicity, computational effectiveness, and the separation of collapse modes for possible different treatments. Second-order cone programming developed for kinematic plastic limit analysis is effectively implemented to study the incremental plasticity collapse mode. The approach is ready to be used to solve general shakedown problems, including those for elastic–plastic kinematic hardening materials and under dynamic loading.     

Motion of Planar Link Mechanisms Revisited

The problem of finding the positions of a four-bar linkage at which the coupler link and rocker have extreme angular velocities is solved. A method is proposed for kinematic analysis of class III mechanisms. The method is based on joining a fictitious link to the original mechanism. The kinematic analysis of a class III mechanism is reduced to successive kinematic analyses of two four-bar linkages     

一类新的超弹性-循环塑性本构模型

目前,很多经典的超弹性-有限塑性本构模型已被提出,但由于超弹性理论中中间构型的引入使得随动硬化法则相对复杂,故多数文献均采用的是经典的Armstrong-Frederick(A-F)随动硬化法则.本文基于已有的本构理论,利用多机制过程的概念拓展了Lion塑性变形分解理论,明确提出了多重中间构型的概念,并在此基础上,对经典理论中客观性的定义进行了概念上的推广,使其更好地适用于超弹性本构理论分析,同时提出了一类新的超弹性-有限塑性本构模型.这类本构模型满足热动力学法则,且可融合多种小变形循环塑性理论中常用的随动硬化法则(如经典的A-F模型,Chaboche模型,Ohno-Wang(O-W)模型以及Karim-Ohno(K-O)模型等),使得小变形理论中背应力的加法分解性质及其演化的临界面阶跃特性在大变形领域中均有所体现,故本文提出的本构理论可看作是小变形循环塑性模型在大变形理论中的扩展.本文最后以K-O模型为例,对推荐模型进行了详细探讨,并与相应的次弹性模型进行了对比.      

Nonlinear Dynamic Stability of Normal and Arthritic Greyhounds

In this paper the dynamic stability of greyhound gait was analyzed within the framework of nonlinear dynamics theory. A video based motion analysis system was utilized to obtain the kinematic data of the hindlimb joints of greyhounds at trot. Phase plane portraits and first return maps for the coxofemoral, femorotibial, and the tarsal joints were calculated from averaged kinematic data for each dog. The analysis was based on the assumption that the steady state dog locomotion could be represented as a nonlinear periodic system. Using the Floquet theory, the dynamic stability of gait was quantified by computing the characteristic multipliers from experimental data. A stability index based on multipliers was used for comparison between normal and arthritic dogs. Phase plane portraits and first return maps of the dogs with transient synovitis were compared with the averaged portraits of the normal dogs. It was observed that the coxofemoral angle exhibited the maximum difference while the femorotibial and the tarsal joints showed little or no difference from those of the normals. Comparison of the Floquet multipliers indicated that the dogs with synovitis had a less stable gait than that of the normal dogs.     

Viscoelastoplastic Deformation of Reinforced Shells of Revolution Under Nonstationary Loading

The elastoviscoplastic behavior of a discretely reinforced shell under axisymmetric nonstationary loading is considered within the framework of the geometrically and physically nonlinear Timoshenko-type theory of shells. The stress–strain state of the structure is studied in terms of the incremental plasticity with kinematic hardening and dynamic yielding condition, which allows for the dynamic viscosity of the structure. The nonstationary behavior of a rigidly fastened reinforced shell under axisymmetric pulse loading normal to the shell surface is considered as an example. The deflection–time and deflection–space relationships are found     

Dynamic system of an engine with spatially rocking links: a mathematical model

A mathematical model of a diesel with swashplates is proposed. The results of studying its design, kinematics, and dynamics are presented. The kinematic chain of the statically determinate mechanism of the engine is schematized. The kinematic relations are obtained taking into account the presence of Hooke’s joints and swashplates. A mathematical model of the dynamic system of the engine is described. A numerical example is given. The kinematics and dynamic processes of the engine are studied     

Nonlinear static and dynamic analysis for laminated,annular, spherical caps of moderate thickness

Based on Timoshenko-Mindlin kinematic hypothesis, the shallow shell theory is extended to include the transverse shear deformation for the nonlinear axisymmetric dynamic analysis of the symmetric cross-ply shallow spherical shell. Using the orthogonal point collocation method and the Newmark scheme, an iterative solution is formulated. The numerical results for the nonlinear static and dynamic responses and dynamic buckling of these shallow spherical shells with circular holes under uniformly distributed static or dynamic normal impact loads are presented and compared with available data.     

Hydroelastic stability of a rectangular plate interacting with a layer of ideal flowing fluid

The three-dimensional formulation of the problem on the natural vibrations and stability of an elastic plate which interacts with a quiescent or flowing fluid is represented and a finite element algorithm of its numerical implementation is proposed. The governing equations, which describe vortex-free ideal fluid dynamics in the case of small perturbations, are written in terms of the perturbation velocity potential and transformed using the Bubnov–Galerkin method. The plate strains are determined on the basis of the Timoshenko theory. The variational principle of virtual displacements which takes into account the work done by inertial forces and the hydrodynamic pressure is used for the mathematical formulation of the dynamic problem of elastic structure. The solution of the problem is reduced to calculations and an analysis of complex eigenvalues of a coupled system of two equations. The effect of the fluid layer height on the eigenfrequencies and the critical velocities of the loss of stability is estimated numerically. It is shown that there exist different types of instability determined by combinations of the kinematic boundary conditions prescribed at the plate edges.     

Failure of a circular reinforced concrete plate against dynamic fluctuating loads

Summary The kinematic shakedown method is used to evaluate the dynamic cyclic collapse loads for a clamped reinforced concrete plate. The method, based on reduced kinematic formulae recently derived by the author, requires determination of the fictitious elastic fields within the plates, in particular – their envelope corresponding to the external loads, and construction of potential incremental collapse mechanisms. The load amplitude-frequency diagrams constructed should help to choose the necessary reinforcements for the plate under given loading conditions. Received 14 January 1998; accepted for publication 25 June 1998     

Non-shakedown collapse of a doubly-reinforced rectangular plate under cyclic loads

A typical doubly-reinforced concrete rectangular plate is subjected to quasi-static (and more general quasiperiodic dynamic) transverse loads. The amount of reinforcements can be different in the upper and lower layers, in the central and rear parts of the plate, and in different directions, as usually designed in practice. An upper bound kinematic approach, which involves construction of potential collapse kinematic fields with plastic hinge lines, is developed to evaluate the non-shakedown loads corresponding to the respective collapse modes. The relations between the non-shakedown load parameters (frequency, amplitude limits) and the reinforcement parameters are derived for practical use. The kinematic assumptions with plastic hinge lines reduce the set of admissible kinematic fields for our upper bound approach, however the procedure appears relatively simple, visual, and can be developed to investigate the behaviour of other plates in various loading and reinforcement schemes, like the respective approach of plastic limit analysis, which was restricted to static loading.     

Finite difference method of transinet nonlinear free surface wave problems

A finite difference method is developed for computing the two-dimensional transient potential flow generated by an impulse on the free surface. Both the dynamic and kinematic free surface conditions are considered in nonlinear version. the primary features of the present paper include the use of special coordinates transformations so that the geometry of the flow field is transformed into a time-invariant region, presents an iteration process, by which the velocity potential is computed as the solution of a Poisson equation, the application of fast Fourier transform (FFT) technique results in a tri-diagonal system of equations which can be readily solved by the Thomas algorithm, the computing time is significantly reduced. Thus an efficient technique for handling the transient potential problems is well justified. The feasibility of the present method has been verified by two examples including different initial disturbances respectively.     

Wave propagation through an interface between viscoelastic media in the presence of defects

The propagation of plane harmonic waves through an interface between viscoelastic media is considered using the equations of field theory of defects, the kinematic identities for an elastic continuum with defects, and the dynamic equations of gauge theory. The reflection and refraction coefficients of elastic displacement waves and the waves of a defect field characterized by a dislocation density tensor and a defect flux tensor are determined. Dependences of the obtained quantities on the parameters of the interfacing media are analyzed.     

Influence of elastic compliance of links on the dynamics and accuracy of a manipulating robot with rotational and translational joints

We pose problems of dynamic and kinematic control of spatial motions for multilink manipulating robot with elastic links and with rotational and translational joints. These problems are reduced to solving a system of ordinary and partial differential equations of hybrid type in the independent variables. We use a numerical integration algorithm for such systems which was developed earlier for manipulating robots with elastic links of anthropomorphic type. We discuss the difficulties arising in mathematical simulation of manipulating robots with simultaneously rotational and translational joints and with elastic links. To perform a comparative analysis and estimate the positional accuracy for the center of mass of the weight transported by the manipulator, we pose problems of dynamic and kinematic control of spatial motions of a manipulating robots with rigid links and with rotational and translational joints. The resolving equations obtained in this case are based on the Lagrange formalism of the second kind. By way of example, we present the solution of dynamic control problems for elastic and rigid two-link manipulators with one translational and two rotational joints.     

Dynamics and control of variable geometry truss manipulator

Variable geometry truss manipulator(VGTM) has potential to work in the future space applications, of which a dynamic model is important to dynamic analysis and control of the system. In this paper, an approach is presented to model the dynamic equations of a VGTM by independent variables, which consists of two double-octahedral truss units and a 3-revolute-prismatic-spherical(3-RPS) parallel manipulator. In this approach, the kinematic recursive relations of two adjacent bodies and geometric constrains are used to deduce the kinematic equations of the VGTM, and Jourdain's velocity variation principle is adopted to establish the dynamic equations of the system. The validity of the proposed dynamic model is verified by comparison of numerical simulations with the software ADAMS. Besides, an active controller for trajectory tracking of the system is designed by the computed torque method. The effectiveness of the controller is numerically proved.     

Nonlinear resonance responses of geometrically imperfect shear deformable nanobeams including surface stress effects

In this work, a thorough investigation is presented into the nonlinear resonant dynamics of geometrically imperfect shear deformable nanobeams subjected to harmonic external excitation force in the transverse direction. To this end, the Gurtin–Murdoch surface elasticity theory together with Reddy’s third-order shear deformation beam theory is utilized to take into account the size-dependent behavior of nanobeams and the effects of transverse shear deformation and rotary inertia, respectively. The kinematic nonlinearity is considered using the von Kármán kinematic hypothesis. The geometric imperfection as a slight curvature is assumed as the mode shape associated with the first vibration mode. The weak form of geometrically nonlinear governing equations of motion is derived using the variational differential quadrature (VDQ) technique and Lagrange equations. Then, a multistep numerical scheme is employed to solve the obtained governing equations in order to study the nonlinear frequency–response and force–response curves of nanobeams. Comprehensive studies into the effects of initial imperfection and boundary condition as well as geometric parameters on the nonlinear dynamic characteristics of imperfect shear deformable nanobeams are carried out through numerical results. Finally, the importance of incorporating the surface stress effects via the Gurtin–Murdoch elasticity theory, is emphasized by comparing the nonlinear dynamic responses of the nanobeams with different thicknesses.