Case Study on the Influence of Kinematic Hardening within a Parameter-free and Non-invasive Form Finding Approach

Inverse form finding – as a type of shape optimization – aims in determining the optimal preform design of a workpiece for a specific forming process, whereby the desired target geometry is known. Recently, a novel parameter-free and heuristic approach was developed to tackle this nonlinear optimization problem. Benchmark tests already delivered promising results. As a particular note-worthy feature of the approach, a coupling to an arbitrary finite element software is feasible in a non-invasive fashion. The aim of this contribution is to investigate the effect of kinematic hardening and cyclic loading on the convergence behavior of the algorithm

A modal approach to hyper-redundant manipulator kinematics

This paper presents novel and efficient kinematic modeling techniques for “hyper-redundant” robots. This approach is based on a “backbone curve” that captures the robot's macroscopic geometric features. The inverse kinematic, or “hyper-redundancy resolution,” problem reduces to determining the time varying backbone curve behavior. To efficiently solve the inverse kinematics problem, the authors introduce a “modal” approach, in which a set of intrinsic backbone curve shape functions are restricted to a modal form. The singularities of the modal approach, modal non-degeneracy conditions, and modal switching are considered. For discretely segmented morphologies, the authors introduce “fitting” algorithms that determine the actuator displacements that cause the discrete manipulator to adhere to the backbone curve. These techniques are demonstrated with planar and spatial mechanism examples. They have also been implemented on a 30 degree-of-freedom robot prototype

Method and apparatus for configuration control of redundant robots

A method and apparatus to control a robot or manipulator configuration over the entire motion based on augmentation of the manipulator forward kinematics is disclosed. A set of kinematic functions is defined in Cartesian or joint space to reflect the desirable configuration that will be achieved in addition to the specified end-effector motion. The user-defined kinematic functions and the end-effector Cartesian coordinates are combined to form a set of task-related configuration variables as generalized coordinates for the manipulator. A task-based adaptive scheme is then utilized to directly control the configuration variables so as to achieve tracking of some desired reference trajectories throughout the robot motion. This accomplishes the basic task of desired end-effector motion, while utilizing the redundancy to achieve any additional task through the desired time variation of the kinematic functions. The present invention can also be used for optimization of any kinematic objective function, or for satisfaction of a set of kinematic inequality constraints, as in an obstacle avoidance problem. In contrast to pseudoinverse-based methods, the configuration control scheme ensures cyclic motion of the manipulator, which is an essential requirement for repetitive operations. The control law is simple and computationally very fast, and does not require either the complex manipulator dynamic model or the complicated inverse kinematic transformation. The configuration control scheme can alternatively be implemented in joint space

Working and Assembly Modes of the Agile Eye

This paper deals with the in-depth kinematic analysis of a special spherical parallel wrist, called the Agile Eye. The Agile Eye is a three-legged spherical parallel robot with revolute joints in which all pairs of adjacent joint axes are orthogonal. Its most peculiar feature, demonstrated in this paper for the first time, is that its (orientation) workspace is unlimited and flawed only by six singularity curves (rather than surfaces). Furthermore, these curves correspond to self-motions of the mobile platform. This paper also demonstrates that, unlike for any other such complex spatial robots, the four solutions to the direct kinematics of the Agile Eye (assembly modes) have a simple geometric relationship with the eight solutions to the inverse kinematics (working modes)

Inference of hot star density stream properties from data on rotationally recurrent DACs

The information content of data on rotationally periodic recurrent discrete absorption components (DACs) in hot star wind emission lines is discussed. The data comprise optical depths tau(w,phi) as a function of dimensionless Doppler velocity w=(Deltalambda/lambda(0))(c/v(infinity)) and of time expressed in terms of stellar rotation angle phi. This is used to study the spatial distributions of density, radial and rotational velocities, and ionisation structures of the corotating wind streams to which recurrent DACs are conventionally attributed. The simplifying assumptions made to reduce the degrees of freedom in such structure distribution functions to match those in the DAC data are discussed and the problem then posed in terms of a bivariate relationship between tau(w, phi) and the radial velocity v(r)(r), transverse rotation rate Omega(r) and density rho(r, phi) structures of the streams. The discussion applies to cases where: the streams are equatorial; the system is seen edge on; the ionisation structure is approximated as uniform; the radial and transverse velocities are taken to be functions only of radial distance but the stream density is allowed to vary with azimuth. The last kinematic assumption essentially ignores the dynamical feedback of density on velocity and the relationship of this to fully dynamical models is discussed. The case of narrow streams is first considered, noting the result of Hamann et al. (2001) that the apparent acceleration of a narrow stream DAC is higher than the acceleration of the matter itself, so that the apparent slow acceleration of DACs cannot be attributed to the slowness of stellar rotation. Thus DACs either involve matter which accelerates slower than the general wind flow, or they are formed by structures which are not advected with the matter flow but propagate upstream (such as Abbott waves). It is then shown how, in the kinematic model approximation, the radial speed of the absorbing matter can be found by inversion of the apparent acceleration of the narrow DAC, for a given rotation law. The case of broad streams is more complex but also more informative. The observed tau(w,phi) is governed not only by v(r)(r) and Omega(r) of the absorbing stream matter but also by the density profile across the stream, determined by the azimuthal (phi(0)) distribution function F-0(phi(0)) of mass loss rate around the stellar equator. When F-0(phi(0)) is fairly wide in phi(0), the acceleration of the DAC peak tau(w, phi) in w is generally slow compared with that of a narrow stream DAC and the information on v(r)(r), Omega(r) and F- 0(phi(0)) is convoluted in the data tau(w, phi). We show that it is possible, in this kinematic model, to recover by inversion, complete information on all three distribution functions v(r)(r), Omega(r) and F-0(phi(0)) from data on tau(w, phi) of sufficiently high precision and resolution since v(r)(r) and Omega(r) occur in combination rather than independently in the equations. This is demonstrated for simulated data, including noise effects, and is discussed in relation to real data and to fully hydrodynamic models