A fluidic-muscle driven force-controlled parallel platform for physical simulation of virtual spatial force-displacement laws

Described in this paper is a six-legged Stewart-Gough parallel platform driven by a relatively new type of fluidic muscles. The advantage of the platform is that it is virtually free of stick-slip effects. Thus, the device is well-suited for fine-tuned force control and for physical simulation of virtual force-displacement laws. The legs of the platform are of type RRPS and are equipped with a coaxial coil spring and a fluidic muscle providing push and pull forces. Each leg is equipped with a force sensor, a pressure sensor, and a magnetostrictive position encoder. The control for the platform consists of six control loops for the six operated actuators with model-based force control comprising individual gas models as well as the rubber nonlinearities for each leg. The control law also includes the gas flow in the proportional directional control valve in 3/3-way function. The present paper describes the basic architecture of the platform, the dynamic models, as well as testbed results for the existing fluidic-muscle parallel platform DynaHex. It is shown that the presented control scheme leads to a stable force control of the platform for quasi-static motion. As an application, the device will be employed in fields of biomechanics, as well as in general environments requiring physical simulation.     

The d-Step Conjecture and Gaussian Elimination

The d-step conjecture is one of the fundamental open problems concerning the structure of convex polytopes. Let Δ (d,n) denote the maximum diameter of a graph of a d-polytope that has n facets. The d-step conjecture Δ (d,2d) = d is proved equivalent to the following statement: For each ``general position' real matrix M there are two matrices drawn from a finite group matrices isomorphic to the symmetric group on d letters, such that has the Gaussian elimination factorization L ^-1 U in which L and U are lower triangular and upper triangular matrices, respectively, that have positive nontriangular elements. If #(M) is the number of pairs giving a positive L ^-1 U factorization, then #(M) equals the number of d-step paths between two vertices of an associated Dantzig figure. One consequence is that #(M)≤ d!. Numerical experiments all satisfied #(M) ≥ 2 ^d-1 , including examples attaining equality for 3 ≤ d ≤ 15. The inequality #(M) ≥ 2 ^d-1 is proved for d=3. For d≥ 4, examples with #(M) =2 ^d-1 exhibit a large variety of combinatorial types of associated Dantzig figures. These experiments and other evidence suggest that the d-step conjecture may be true in all dimensions, in the strong form #(M) ≥ 2 ^d-1 . Received April 10, 1995, and in revised form August 23, 1995.     

Thermotropic copolyesters. III. Synthesis and characterization of liquid crystal copolyesters containing the bicyclo[2.2.2]octane ring system

A number of thermotropic copolyesters which contain the bicylo[2.2.2]octane ring system have been synthesized. Because of the stiffening effect of the bicyclo[2.2.2]octane group on the chain, the sebacoyl spacer was used to obtain meltable compositions.     

An algebraic approach to the restoration of images

Two different matrix algorithms are described for the restoration of blurred pictures. These are illustrated by numerical examples.     

The polarography of oximes: II. 1,2-Acenaphthaquinone monoxime

Polarography of 1,2-acenaphthaquinone monoxime has been carried out in buffers (pH 3.5–13.0) of constant ionic strength 0.5 M and 40% alcohol $\text{v}\text{v}$ at 25 ± 0.5 °C. The oxime group underwent diffusion-controlled reduction (4e) over the whole pH range. The number of electrons involved in the reduction was found by coulometric method as well as by incorporating the values of diffusion coefficients, obtained by using a McBain-Dawson cell, into the Ilkovi? equation. Koutecky's method has been used to compute the kinetic parameters (αn_aand ?log K_f.h) for the reduction of the oxime group and a reduction mechanism is proposed.     

Alcoholate complexes of chromium(III) chloride

Summary A number of alcoholate complexes of chromium chloride with the general formula, CrCl₃ · xROII (R = Me, Et, i-Pr, n-Bu and n-Ilexyl; x = 3 and 4) have been synthesized by the reactions of CrCl₃ · 3 TIIF with an excess of the appropriate alcohols under reflux. Physicochemical studies such as i.r., visible reflectance, electron spin resonance spectra and thermogravimetric measurements, in addition to elemental analyses, throw light on the structure of these complexes.