The octahedral manipulator revisited

Abstract

Abstract-In most practical implementations of the GoughStewart platform, the octahedral form is either taken as it stands or is approximated. The kinematics of this particular instance of the Gough-Stewart platform, commonly known as the octahedral manipulator, has been thoughtfully studied. It is well-known, for example, that its forward kinematics can be solved by computing the roots of an octic polynomial and its singularities have a simple geometric interpretation in terms of the intersection of four planes in a single point. In this paper, using a distance-based formulation, it is shown how these properties can be derived without relying neither on variable eliminations nor trigonometric substitutions. Moreover, thanks to this formulation, a family of platforms kinematically equivalent to the octahedral manipulator is obtained. Herein, two Gough-Stewart parallel platforms are said to be kinematically equivalent if there is a one-to-one correspondence between their squared leg lengths for the same configuration of their moving platforms with respect to their bases. If this condition is satisfied, it can be shown that both platforms have the same assembly modes and their singularities, in the configuration space of the moving platform, are located in the same place.

Flexible robotic device for spinal surgery

“…The tools could be hand-held and manipulated by a surgeon, but there is an intrinsic problem with fatigue in the human hand during longer length procedures [18]. To overcome this, a parallel manipulator robotic platform, which is also called the octahedral platform [145] (OP), has been designed that acts as a mount for the tools (T), and produces the desired range…”

Kinematically Redundant Octahedral Motion Platform for Virtual Reality Simulations

“…But we pursue another strategy for the technical realization; namely the usage of a design which is totally free of double joints but kinematically equivalent to the octahedral manipulator (cf. [20]). Therefore the resulting design illustrated in Fig.…”

Closed-form position analysis of variable geometry trusses

“…A truss is a structure where each element, typically a bar, only supports tension or compression forces because it is connected to other bars through what are assumed to be multiple spherical joints [1], although in some cases the joints may be separated in the actual construction [2,3]. While rigid trusses have been widely used in construction, passive mobile trusses are commonly used, for instance, as shock absorbers.…”

“…This is why variable geometry trusses are sometimes considered a generalization of the serial/parallel robots [5]. Due to their exceptional stiffness to weight ratio, References [14] [15], [3] [16] [17] their structural simplicity, and their shape versatility, variable geometry trusses have a myriad of potential applications including robot arms [6], hyper-redundant manipulators [7], flight simulators [8], payload vibration reduction systems [9], tools to manipulate large payloads [10], morphing wings [11], space devices [12] or civil engineering structures [13]. The design of novel variable geometry trusses rely on having a complete kinematics characterization of their constituent cells.…”

“…Unfortunately, even with compact formulations, the elimination process gets rapidly involved as the order of the bipyramid increases. Therefore, up to now, only closed-form solutions for the octahedral [15,3] and the decahedral bipyramids [16] are available. For these two cases, it has been shown that the univariate closure polynomials are of degree 8 and 24, respectively.…”