Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Classification of all self-motions of the original Stewart-Gough platform
The original Stewart-Gough (S-G) platform is a parallel 6-6 mechanism with both bases being isosceles triangles cut at the vertices. All six points of the upper base are connected by telescopic legs with six points of the lower base by spherical joints. If the length of all six legs remains constant then the S-G platform is stiff. Exceptions from this rule are called self-motions (or Borel-Bricard motions) of the S-G platform. We have determined all self-motions of the original S-G platform. As a by-product, new types of Borel-Bricard motions have been discovered. During this task, one has to use a computer for three different purposes. First, algebraic equations of self-motions have to be determined. For this, we have used Maple V on a workstation. After the equations of self-motion have been derived, one has to visualize the result, which means plotting trajectories of points of the platform and corresponding positions of the upper base. If the motion can be parameterized, we can plot trajectories by a suitable graphical system. If it cannot be parameterized, we have to numerically compute some locations of the upper base of the platform and then interpolate them. Self-motions of the original S-G platform can be translatory motions, pure rotations, generalized screw motions with a fixed axis, spherical four-bar mechanisms or more general space motions. One of the special cases of the general self-motion is a space motion with three circular trajectories, which is not spherical. This motion yields a new spatial mechanism, which is a spatial analogy of the well-known planar or spherical four-bar mechanisms.
Classification of all self-motions of the original Stewart-Gough platform
The original Stewart-Gough (S-G) platform is a parallel 6-6 mechanism with both bases being isosceles triangles cut at the vertices. All six points of the upper base are connected by telescopic legs with six points of the lower base by spherical joints. If the length of all six legs remains constant then the S-G platform is stiff. Exceptions from this rule are called self-motions (or Borel-Bricard motions) of the S-G platform. We have determined all self-motions of the original S-G platform. As a by-product, new types of Borel-Bricard motions have been discovered. During this task, one has to use a computer for three different purposes. First, algebraic equations of self-motions have to be determined. For this, we have used Maple V on a workstation. After the equations of self-motion have been derived, one has to visualize the result, which means plotting trajectories of points of the platform and corresponding positions of the upper base. If the motion can be parameterized, we can plot trajectories by a suitable graphical system. If it cannot be parameterized, we have to numerically compute some locations of the upper base of the platform and then interpolate them. Self-motions of the original S-G platform can be translatory motions, pure rotations, generalized screw motions with a fixed axis, spherical four-bar mechanisms or more general space motions. One of the special cases of the general self-motion is a space motion with three circular trajectories, which is not spherical. This motion yields a new spatial mechanism, which is a spatial analogy of the well-known planar or spherical four-bar mechanisms.
Classification of all self-motions of the original Stewart-Gough platform
Karger, A. (Autor:in) / Husty, M. (Autor:in)
Computer Aided Design ; 30 ; 205-215
1998
11 Seiten, 11 Quellen
Aufsatz (Zeitschrift)
Englisch
Revisiting Stewart–Gough platform applications: A kinematic pavilion
| Elsevier | 2021
| British Library Online Contents | 2008