Kinematic and Dynamic Analysis of Mechanisms. A Finite Element Approach Based on Euler Parameters

Géradin, Michel; Robert, Gerardo González; Buchet, P.

doi:10.1007/978-3-642-82704-4_3

Cited by 14 publications

(7 citation statements)

References 4 publications

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“…Beam curvatures are represented either by the skew-symmetric tensor (: ) or axial vector in spatial form or material form, respectively, And the centroidal line strains are represented by vector in spatial or material form, respectively, Inserting the basic kinematic relations (l), (3) and (4) into the definition of the deformation gradient tensor of the beam, following expressions are derived:…”

Section: Beam Equationsmentioning

confidence: 99%

Geometrically Non-Linear and Elastoplastic Three-Dimensional Shear Flexible Beam Element of Von-Mises-Type Hardening Material

Park

Lee

1996

Int. J. Numer. Meth. Engng.

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SUMMARYA three-dimensional elastoplastic beam element being capable of incorporating large displacement and large rotation is developed and examined. Elastoplastic constitutive equations are applied to the beam element based upon the assumption of small deformational strain leading to a material formulation which is completely objective for the application of stress update procedures. The continuum-type equations of plastic model of J, mixed hardening are transformed into the beam equations by satisfying beam hypotheses. An effective stress update algorithm is proposed to integrate elastoplastic rate equations by means of the so-called multistep method which is a method of successive control of residuals on yield surfaces. It avoids severe divergence when the displacement increments become large which is usual for the continuation methods. Material tangent stiffness matrix is derived by using consistent elastoplastic modulus resulting from the integration algorithm and is combined with geometric tangent stiffness matrix. Different from other elements, the present element is shear flexible and can satisfy the plasticity condition in a pointwise fashion. A great number of numerical examples are analysed and compared with the literature. The proposed beam element is verified to be not only quite accurate but also very effective for the analyses of pre-buckling and large deflection collapse of spatial framed structures.

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Section: Beam Equationsmentioning

confidence: 99%

Geometrically Non-Linear and Elastoplastic Three-Dimensional Shear Flexible Beam Element of Von-Mises-Type Hardening Material

Park

Lee

1996

Int. J. Numer. Meth. Engng.

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“…The situation is represented geometrically by Figure 2. where and where gives linearized increments in TR(*)S0 (3). Note that the addition has meaning since Y and @(A) belong to the same vector space.…”

Section: T R S O (~) = { 8 R / 8~s O ( 3 ) } = { R~/~) E S O (~) }mentioning

confidence: 99%

“…We remark that the stiffness matrix so computed is symmetric; this property is assured because the differentiation of the rotational terms is now made with respect to parameters that lie in a vector space, the tangent space TlSO (3).…”

Section: A Iy=o= -Z Vmentioning

confidence: 99%

“…The three-dimensional rotations representation problem can be treated from a differential geometry point of view. ' ' 9 Proper orthogonal transformations constitute a non-conmutative (Lie) group referred to as the special orthogonal group SO(3) and every system of parametrization is a projection from SO(3) onto a specific tangent vector space to SO (3).…”

Section: Introductionmentioning

confidence: 99%

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A beam finite element non‐linear theory with finite rotations

Cardona

Géradin

1988

Numerical Meth Engineering

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548

351

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“…For the hinge element, three deformation functions are defined, namely a large relative rotation about the element axis denoted e (k) 1 and two small orthogonal bending deformations denoted (k) 2 and (k) 3 respectively. For a detailed description of the hinge element, the reader is referred to Geradin et al, 1986 andSchwab andMeijaard, 1999. The motor hinge represents the driving system which generates the net driving torque τ (k) . The relative rotation e 3 of the motor hinge are prescribed to be zero.…”

Section: Joint Modelmentioning

confidence: 99%

Modelling and Identification of Robots with Joint and Drive Flexibilities

Hardeman

Aarts

Jonker

IUTAM Symposium on Vibration Control of Nonlinear Mechanisms and Structures

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Modelling and identification of flexible-joint robots is required for dynamic simulation and model based control of industrial robots. A nonlinear finite element based method is used to derive the dynamic equations of motion in a form suitable for both simulation and identification. The latter requires that the equations of motion are linear in the dynamic parameters. For accurate simulations of the robot tip motion, the model should describe the relevant dynamic properties such as joint friction and flexibilities. Both the drive and the joint flexibilities are included in the model. Joint friction is described by means of a static friction model, including Coulomb and viscous friction components. The dynamic parameters describing mass, inertia, stiffness, damping and friction properties are obtained from a least squares solution of an over determined linear system assembled from closed loop identification experiments. In the identification experiment, the robot moves along a prescribed trajectory while all joint angles, flexible deformations and driving torques are recorded. To excite joint vibrations during the identification feed forward torques at frequencies above the bandwidth of the control system are superposed on the joint torques. The applicability of the method is demonstrated in a numerical study of a four-link industrial robot.

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Kinematic and Dynamic Analysis of Mechanisms. A Finite Element Approach Based on Euler Parameters

Cited by 14 publications

References 4 publications

Geometrically Non-Linear and Elastoplastic Three-Dimensional Shear Flexible Beam Element of Von-Mises-Type Hardening Material

Geometrically Non-Linear and Elastoplastic Three-Dimensional Shear Flexible Beam Element of Von-Mises-Type Hardening Material

A beam finite element non‐linear theory with finite rotations

Modelling and Identification of Robots with Joint and Drive Flexibilities

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