Qimi Jiang

The Maximal Singularity-Free Workspace of the Gough–Stewart Platform for a Given Orientation

The maximal singularity-free workspace of parallel mechanisms is a desirable criterion in robot design. However, for a 6DOF parallel mechanism, it is very difficult to find an analytic method to determine the maximal singularity-free workspace around a prescribed point for a given orientation. Hence, a numerical algorithm is presented in this paper to compute the maximal singularity-free workspace as well as the corresponding leg length ranges of the Gough-Stewart platform. This algorithm is based on the relationship between the maximal singularity-free workspace and the singularity surface. Case studies with different orientations are performed to demonstrate the presented algorithm. The obtained results can be applied to the geometric design or parameter (leg length) setup of this type of parallel robots.

Evaluation and Representation of the Theoretical Orientation Workspace of the Gough–Stewart Platform

The evaluation and representation of the orientation workspace of robotic manipulators is a challenging task. This work focuses on the determination of the theoretical orientation workspace of the Gough-Stewart platform with given leg length ranges [ρ min i , ρ max i ]. By use of the roll-pitch-yaw angles (Φ, θ, ψ), the theoretical orientation workspace at a prescribed position P 0 can be defined by up to 12 workspace surfaces. The defined orientation workspace is a closed region in the 3D orientation Cartesian space OΦθψ. As all rotations R(x, Φ), R(y, 0), and R(z, ψ) take place with respect to the fixed frame, any point of the defined orientation workspace provides a clear measure for the platform to, respectively, rotate in order around the (x,y,z) axes of the fixed frame. An algorithm is presented to compute the size (volume) of the theoretical orientation workspace and intersectional curves of the workspace surfaces. The defined theoretical orientation workspace can be applied to determine a singularity-free orientation workspace.

Singularity Equations of Gough–Stewart Platforms Using a Minimal Set of Geometric Parameters

So far, in the derivation of the singularity equations of Gough–Stewart platforms, all researchers defined the mobile frame by making its origin coincide with the considered point on the platform. One problem can be that the obtained singularity equation contains too many geometric parameters and is not convenient for singularity analysis, especially not convenient for geometric optimization. Another problem can be that the obtained singularity equation cannot be used directly in practice. To solve these problems, this work presents a new approach to derive the singularity equation of the Gough–Stewart platform. The main point is that the origin of the mobile frame is separated from the considered point and chosen to coincide with a special point on the platform in order to minimize the geometric parameters defining the platform. Similarly, by defining a proper fixed frame, the geometric parameters defining the base can also be minimized. In this way, no matter which practical point of the platform is chosen as the considered point, the obtained singularity equation contains only a minimal set of geometric parameters and becomes a solid foundation for the geometric optimization based on singularity analysis.

The Maximal Singularity-Free Workspace of Planar 3-RPR Parallel Mechanisms

To avoid kinematic singularities inside the workspace of parallel mechanisms is a basic requirement in robot design. This paper addresses the case of planar 3-RPR parallel mechanisms. By investigating the singularity equation, it is discovered that the singularity locus of any point on the platform is a circle, if the base and the platform are similar triangles. Furthermore, the centres of three circles for workspace have been proved to lie exactly on the singularity circle. With these useful information, the leg length ranges can be determined by analyzing the workspace. For a base of unit area, it is found that robots with equilateral triangle base and platform can obtain the maximal singularity-free workspace. Three case studies demonstrate this result. Finally, a geometric design procedure for this type of robot is proposed and an example is provided

Maximal Singularity-Free Total Orientation Workspace of the Gough-Stewart Platform

The maximal singularity-free total orientation workspace is highly desirable in a context of design of parallel robots. In practice, this type of workspace is interesting because a parallel robot often works in a given range of orientations. In this work, an algorithm is presented to compute the maximal singularity-free total orientation workspace of the Gough-Stewart platform. In order to demonstrate the presented algorithm, an example is provided.

Geometric Optimization of the MSSM Gough–Stewart Platform

This work focuses on analyzing the effects of the geometric parameters on the singularity-free workspace in order to determine the optimal architecture for the minimal simplified symmetric manipulator Gough-Stewart platform. To this end, the reference orientation is taken as the considered orientation because it is an impartial orientation. In this orientation, the singularity surface becomes a plane coinciding with the base plane. Accordingly, an analytic algorithm is developed to determine the singularity-free workspace. The analysis shows that: (1) for similar isosceles triangle base and platform, the optimal architecture is one for which both the base and the platform are equilateral triangles, and the size ratio between the platform and the base is 1/2; and (2) if the base and the platform are not similar triangles, the global optimal architecture is difficult to determine. Only an approximate optimal architecture is available.

Dynamic Optimization of Reactionless Four-Bar Linkages

Reactionless mechanisms have many important applications because of their zero reaction forces and moments at the base. However, in most cases, these mechanisms consume more energy than their unbalanced counterparts. This paper focuses on analyzing the relationship between the needed input torque and the dynamic parameters of reactionless four-bar linkages. The objective is to minimize the needed input torque by optimizing the relevant dynamic parameters. The dynamic analysis shows that the needed input torque mainly depends on the mass of the link, which needs to be balanced. The results obtained can be applied to the design optimization and dynamic control of the devices such as parallel manipulators composed of reactionless four-bar linkages.

Effects of Orientation Angles on the Singularity-Free Workspace and Orientation Optimization of the Gough–Stewart Platform

The singularity-free workspace of parallel mechanisms is highly desirable in a context of robot design. This work focuses on analyzing the effects of the orientation angles on the singularity-free workspace of the Gough–Stewart platform in order to determine the optimal orientation. In any orientation with ϕ=θ=0 deg and ψ≠±90 deg, the singularity surface becomes a plane coinciding with the base plane. Hence, an analytic algorithm is presented in this work to determine the singularity-free workspace. The results show that the singularity-free workspace in some orientations can be larger than that in the reference orientation with ϕ=θ=ψ=0 deg. However, the global optimal orientation is difficult to determine. Only an approximate optimal orientation is available. The results obtained can be applied to the design or parameter setup of the Gough–Stewart platform.

Singularity Equations of Gough-Stewart Platforms Using a Minimal Set of Geometric Parameters

So far, in the derivation of the singularity equations of Gough-Stewart platforms, all research works defined the mobile frame by making its origin coincide with the considered point on the platform. One problem can be that the obtained singularity equation contains too many geometric parameters and is not convenient for singularity analysis, especially not convenient for geometric optimization. Another problem can be that the obtained singularity equation cannot be used directly in practice. To solve these problems, this work presents a new approach to derive the singularity equation of the Gough-Stewart platform. The main point is that the origin of the mobile frame is separated from the considered point and chosen to coincide with a special point of the platform in order to minimize the geometric parameters defining the platform. Similarly, by defining a proper fixed frame, the geometric parameters defining the base can also be minimized. In this way, no matter which practical point of the platform is chosen as the considered point, the obtained singularity equation contains only a minimal set of geometric parameters and becomes a solid foundation for the geometric optimization based on singularity analysis.Copyright

Maximal singularity-free orientation workspace over a position region of Gough–Stewart platform

Maximizing the singularity-free workspace of parallel manipulators is highly desirable in a context of robot design. So far, no work has been found to address the maximal singularity-free orientation workspace over a position region. In practice, this type of workspace is interesting because a mechanism often works in a range of positions. This work focuses on the Gough–Stewart platform. An optimal position at which the mechanism holds the maximal singularity-free orientation workspace is determined. This optimal position lies on the line which is perpendicular to the base and passes the centroid of the base. Considering the symmetry, a parallelepiped with centre at the determined optimal position could be an interesting working position region for the Gough–Stewart platform. Two algorithms are presented to compute the maximal singularity-free orientation workspace over such an interesting position region. An example is provided for demonstration.