Elastic Multibody Dynamics

Bremer, Hartmut

doi:10.1007/978-1-4020-8680-9

Cited by 106 publications

(32 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There the system Jacobian is called the "natural orthogonal complement", motivated by the fact that the columns of J b are orthogonal to the vectorial representations of constraint wrenches (although the former are screws, whereas the latter are coscrews). In classical vector notation, they were reported in [39,48] and [14]. In [39] the equations (79) are called "partial velocities" [40].…”

Section: Euler-jourdain Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Screw and Lie group theory in multibody dynamics

Müller

2017

Multibody Syst Dyn

View full text Add to dashboard Cite

Screw and Lie group theory allows for user-friendly modeling of multibody systems (MBS), and at the same they give rise to computationally efficient recursive algorithms. The inherent frame invariance of such formulations allows to use arbitrary reference frames within the kinematics modeling (rather than obeying modeling conventions such as the Denavit-Hartenberg convention) and to avoid introduction of joint frames. The computational efficiency is owed to a representation of twists, accelerations, and wrenches that minimizes the computational effort. This can be directly carried over to dynamics formulations. In this paper, recursive O(n) Newton-Euler algorithms are derived for the four most frequently used representations of twists, and their specific features are discussed. These formulations are related to the corresponding algorithms that were presented in the literature. Two forms of MBS motion equations are derived in closed form using the Lie group formulation: the so-called Euler-Jourdain or "projection" equations, of which Kane's equations are a special case, and the Lagrange equations. The recursive kinematics formulations are readily extended to higher orders in order to compute derivatives of the motions equations. To this end, recursive formulations for the acceleration and jerk are derived. It is briefly discussed how this can be employed for derivation of the linearized motion equations and their time derivatives. The geometric modeling allows for direct application of Lie group integration methods, which is briefly discussed.

show abstract

Section: Euler-jourdain Equationsmentioning

confidence: 99%

“…In Sect. 5.1, the Euler-Jourdain respectively "projection" equations [14,84] are presented that, together with the screw formulation of MBS kinematics, allow for an efficient MBS modeling in terms of readily available geometric data. In Sect.…”

Section: Introductionmentioning

confidence: 99%

Screw and Lie group theory in multibody dynamics

Müller

2017

Multibody Syst Dyn

View full text Add to dashboard Cite

show abstract

“…This formulation considers the deformation of flexible structures that are subjected to external loads and undergo a large reference motion [4,19,25]. This approach has been introduced in various multibody codes such as Simpack and is also available as a library in the modeling language Modelica [12], which is used at the Institute of System Dynamics and Control at DLR.…”

Section: Motivationmentioning

confidence: 99%

Moving loads on flexible structures presented in the floating frame of reference formulation

Hartweg

Heckmann

2016

Multibody Syst Dyn

View full text Add to dashboard Cite

The introduction of moving loads in the Floating Frame of Reference Formulation is presented. We derive the kinematics and governing equations of motion of a general flexible multibody system and their extension to moving loads. The equivalence of convective effects with Coriolis and centripetal forces is shown. These effects are measured numerically and their significance in moving loads traveling at high speed is confirmed. A method is presented to handle discontinuities when moving loads separate from the flexible structure. The method is extended from beam models to general flexible structures obtained by means of the Finite Element Method. An interpolation method for the deformation field of the modal representation of these bodies is introduced.The work is concluded by application of the method to modern mechanical problems in numerical simulations.

show abstract

“…Therefore, a multibody dynamics model M(q)q+h(q,q) = Q for the complete robot was derived, based on the Projection Equation in subsytem formulation [4]. A rotating arm was used as the main subsystem with basically the same parameter set as To compensate for model errors and parameter uncertainties, a disturbance torque observer with design parameter K O,i ,…”

Section: Mechnical Modeling and Position Controlmentioning

confidence: 99%

Modeling and Control of a Seven Axes Hybrid Electric/Pneumatic Robot Arm

Kastner

Gattringer

Bremer

et al. 2011

Proc Appl Math and Mech

View full text Add to dashboard Cite

Passively compliant drive concepts are often used in bio-inspired robot designs. Especially fluidic artificial muscles share many characteristics with their natural counterparts. Industrial manipulators can benefit from the increased robustness and safety (in contrast to rigid drives) especially in cooperative human/robot environments. We compare different model-based control concepts for a single rotational joint actuated by two fluidic muscles in combination with proportional valves. While the complete valve and muscle models are already included in this setup, the mechanical model becomes more complex when we extend the control to a full seven axes articulated robot arm with both, electrically and pneumatically actuated joints. In this case the Projection Equation in subsystem description is used for the multibody model, allowing a straight-forward realtime application to different robot kinematics. Remaining model errors and disturbances are handled by observer algorithms. We present measurement results and compare them to simulation outputs. Besides the position control, possible approaches for sensorless external force estimation are discussed. They take advantage of the compliance of the robot and are again based on the actuator and multibody models. The considered robot (see Figure 1) is mainly actuated by so-called pneumatic artificial muscles (PAM) [1] -fibre reenforced rubber tubes, which contract when filled with air. The static pulling muscle force F can be modeled by, where p is the internal pressure, h the muscle contraction and a(h) and b(h) are polynomials used to approximate the nonlinear relation between the contraction and the force.A pneumatic rotational joint is actuated by two antagonistically arranged PAMs 1 and 2. The contractions, h 1/2 = h 0 ± r/l (q − q 0 ) 100 %, are both uniquely defined by the joint angle q and construction parameters (acting radius r, muscle length l, angle q 0 , where both muscles have the same contraction h 0 ). The generated torque Q = r (F 1 −F 2 ) is affine in the pressures and can be written as Q = A(q) 0.5 (p 1 + p 2 ) + B(q) (p 1 − p 2 ) + C(q) with some functions A, B and C, which can be calculated from the single muscle characteristics or identified pointwise on the real system. Figure 2 shows the comparison between the measured (thick line) and the nominal muscle model (thin line). A locally (only around Q 1 = 0) calibrated model (light line) has been added for reference. The validation maneuver used in this figure is a slow left/right movement, which means that the actual torque is always close to zero. Beside the differences in the models, a common hysteresis loop is visible in all three curves. This is not yet accounted for in our model and will be subject to further research.The underlying control loop for the muscle pressures is flatness based (see, for example [3]) with the pressure dynamicṡ p V + pV =ṁ R S T . The current muscle volume V depends only on the contraction and can therefore also be calculated from the joint angle. The absolute temper...

show abstract

Elastic Multibody Dynamics

Cited by 106 publications

References 0 publications

Screw and Lie group theory in multibody dynamics

Screw and Lie group theory in multibody dynamics

Moving loads on flexible structures presented in the floating frame of reference formulation

Modeling and Control of a Seven Axes Hybrid Electric/Pneumatic Robot Arm

Contact Info

Product

Resources

About