The first three symmetric mode frequencies are 1. The first two frames are used for the chassis and the pylon. Combining several bodies to one subsystem needs to define one reference frame. Typical subsystems for such robots contain a motor, an elastic gear, an elastic link and a tip mass. Printed on acid-free paper 987654321 springer. They should not be mixed up with the the impressed forces. The reason for this statement is, of course, that a calculation by hand allows for a limited number of degrees of freedom only.
Elastic Multibody Systems Considering pure elastic multibody systems, the Projection Equation is obtained by splitting the overall sum in eq. The results were then tabulated for different trajectories which entered the real-time closed-loop control, e. The results have been obtained with two shape functions for each subsystem. As a consequence, the series converges rapidly with one dominant component for every eigenvector xn in eq. At that time, quite an amount of effort was spent in the derivation of the motion equations just for one special case The tremendous advance in computer science. The shape functions used here are theoretically not restricted to a plate with free edges.
This paper presents the analysis and control of a mobile platform which uses a novel steering principle. Here, the closed loop control becomes indispensable. All remaining points which fill up the rigid body volume are then to be defined via additional assumptions mass distribution. See also the remark on p. The method is applied to rigid multibody systems where the rigid body is defined such that, by relaxation of the rigidity constraints, one can directly proceed to elastic bodies.
However, Jacobi tried to find a mathematical proof for a mechanical principle and Poinsot attempted to deal with scientific falsehoods. Here, it is most instructive to follow W. Simulations as well as experimental results are presented. Concentrating on these, one has for eq. This review article has 55 references. Tabak, George Mason University, Fairfax, Virginia, U.
Their reactions can, of course, not always be neglected. Approximations bold hed by their number of nodes. On the basis of Lagrange's Principle, it presents a Central Equation of Dynamics that yields a unified view on existing methods in dynamics. It will therefore be suitable to reconsider the resulting equations and look for simplifications. Boltzmann, 1890 , physicists turned to the construction of equations or systems of equations that allowed one to calculate real phenomena without any interpretation of the physical reality. Index dm is suppressed in eq.
The mass matrix of a mechanical system endows the configuration manifold with the structure of a Riemannian manifold and provides an isomorphism between the tangent space and the cotangent space at each point of the configuration manifold. We therefore consider the terms minimal coordinate and minimal velocity better suited for our context. Finally, a second problem concerning fluidstructure effects is also studied numerically. Elastic deflections are thus v ξ, t and ϑ ξ, t where ξ is the beam length coordinate. Or the other way round: the shorter the mathematical representation, the more effort in evaluating motion equations. In that case, it will be suitable to make use of the block- triangular form of the functional matrix in the sense of a Gaussian elimination algorithm.
Results from Classical Optimization Theory Comment: In Table 8. The method is applied to rigid multibody systems where the rigid body is defined such that, by relaxation of the rigidity constraints, one can directly proceed to elastic bodies. In the present case, it is reduced to pure elastic components in order to separate the rigid body coordinates from the elastic deflections. As the canonical equations show left column we furthermore presume steadiness. Finally a comparison between this and existing realtime capable time-optimal trajectory planning methods is drawn using a six degree-of-freedom serial robot.
Using the example of a planar manipulator, the presented method is shown to outperform conventional optimal control approaches regarding robustness and the resulting trajectory characteristics. This does not mean that we are writing history. The kinematics is analyzed and a kinematic model is derived. This is a typical task for the computer. The gripper is characterized by mGr. Here, ϕ the general expression ω r is used to emphasize that the relative velocities due to elastic deformation are integrable.
The operator D as well as the ones for the dynamical boundary conditions are no longer needed. Although plane motion is a rather simple case, it can nevertheless give insight for those readers who prefer quick reading without trespassing on the previous chapters in detail. Background This textbook is an introduction to and exploration of a number of core topics in the? Diese Gewichtsreduktion führt aber auch auf einen Steifigkeitsverlust und damit zu einem schwingungsanf älligen System. For the weak formulation of elastic multibody systems, however, we prefer the notation according to eq. Experimentelle Ergebnisse zeigen die Wirksamkeit der vorgeschlagenen Verfahren. In the co-rotating frame Damping. And it is, in this interpretation, no longer a virtual velocity but a virtual displacement.