The Stewart Platform of General Geometry Has 40 Configurations

1993 ◽  
Vol 115 (2) ◽  
pp. 277-282 ◽  
Author(s):  
M. Raghavan
Keyword(s):  
Numerical Technique ◽  
Stewart Platform ◽  
Multivariate Polynomial ◽  
Prismatic Joint ◽  
Flight Simulators ◽  
Arbitrary Complex ◽  
Set Up ◽  
General Geometry ◽  
Six Degree Of Freedom ◽  
Robotic Applications

The Stewart platform is a six-degree-of-freedom, in-parallel linkage. It is used in automotive and flight simulators, positioning tables for assembly and robotic applications, and various other applications requiring linkages with high structural stiffness. It consists of a base link, a coupler link, and six adjustable-length legs supporting the coupler link. Each leg consists of a prismatic joint with ball-joint connections to the base and coupler, respectively. The forward kinematics problem for the Stewart platform may be stated as follows: given the values of the six prismatic joint displacement inputs to the linkage, compute the position and orientation of the coupler link. This problem may be set up as a system of nonlinear multivariate polynomial equations. We solve this problem using a numerical technique known as polynomial continuation. We show that for Stewart platforms of general geometry (i.e., platforms in which the linkage parameters are arbitrary complex numbers) this problem has 40 distinct solutions.

The Stewart Platform of General Geometry Has 40 Configurations

1991 ◽  
Author(s):  
Madhusudan Raghavan
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Technique ◽  
Stewart Platform ◽  
Multivariate Polynomial ◽  
Six Degrees Of Freedom ◽  
Prismatic Joint ◽  
Flight Simulators ◽  
Set Up ◽  
General Geometry ◽  
Robotic Applications

Abstract The Stewart platform is a six-degrees-of-freedom, in-parallel linkage. It is used in automotive and flight simulators, positioning tables for assembly and robotic applications, and various other applications requiring linkages with high structural stiffness. It consists of a base link, a coupler link, and six adjustable-length legs supporting the coupler link. Each leg consists of a prismatic joint with ball-joint connections to the base and coupler respectively. The forward kinematics problem for the Stewart platform may be stated as follows: given the values of the six prismatic joint displacement inputs to the linkage, compute the position and orientation of the coupler link. This problem may be set up as a system of nonlinear multivariate polynomial equations. We solve this problem using a numerical technique known as polynomial continuation. We show that for Stewart platforms of general geometry (i.e., platforms in which the linkage parameters are arbitrary complex numbers) this problem has 40 distinct solutions.

An Algebraic Method for Direct Position Analysis of the General Stewart Platform Manipulator Robot

2009 ◽  
Vol 626-627 ◽  
pp. 405-410
Author(s):  
Xi Guang Huang ◽  
Guang Pin He ◽  
Q.Z. Liao
Keyword(s):  
Parallel Manipulator ◽  
Algebraic Method ◽  
Stewart Platform ◽  
Mobile Platform ◽  
Analysis Problem ◽  
Position Analysis ◽  
General Geometry ◽  
Six Degree Of Freedom ◽  
Manipulator Robot ◽  
Base Platform

Stewart platform manipulator robot is a six degree of freedom, parallel manipulator, which consists of a base platform, a mobile platform and six limbs connected at six distinct points on the base platform and the mobile platform respectively. The direct position analysis problem of Stewart platform relates to the determination of the mobile platform pose for a given set of the lengths of the limbs. In this paper, we present a concise algebraic method for solving the direct position analysis problem for the fully parallel manipulator with general geometry, often referred to as General Stewart platform manipulator. Based on the presented algebraic method, we derive a 40th degree univariate polynomial from a determinant of 20×20 Sylvester’s matrix, which is relatively small in size. We also obtain a complete set of 40 solutions to the most general Stewart platform. The proposed method is comparatively concise and reduces the computational burden. Finally the method is demonstrated by a numerical example.

Analytic Form of the Six-Dimensional Singularity Locus of the General Gough-Stewart Platform

2004 ◽  
Author(s):  
Haidong Li ◽  
Cle´ment M. Gosselin ◽  
Marc J. Richard ◽  
Boris Mayer-St-Onge
Keyword(s):  
Analytic Form ◽  
Stewart Platform ◽  
Jacobian Matrices ◽  
Analytical Expression ◽  
Flight Simulators ◽  
Velocity Equation ◽  
Singularity Locus ◽  
Important Design ◽  
Robotic Applications

The determination of the 6-D singularity locus of the general Gough-Stewart platform is discussed in this article. The derivation of the velocity equation and the corresponding Jacobian matrices is first presented. Then a new procedure is introduced to obtain the analytical expression of the singularity locus, which is a function of six variables (x, y, z, φ, θ, ψ), using the velocity equation. Examples are also given to illustrate the results obtained. Gough-Stewart platforms can be used in several robotic applications as well as in flight simulators. The determination of the singularity locus is a very important design and application issue.

Analytic Form of the Six-Dimensional Singularity Locus of the General Gough-Stewart Platform

2005 ◽  
Vol 128 (1) ◽  
pp. 279-287 ◽  
Author(s):  
Haidong Li ◽  
Clément M. Gosselin ◽  
Marc J. Richard ◽  
Boris Mayer St-Onge
Keyword(s):  
Analytic Form ◽  
Stewart Platform ◽  
Jacobian Matrices ◽  
Analytical Expression ◽  
Flight Simulators ◽  
Velocity Equation ◽  
Singularity Locus ◽  
Important Design ◽  
Robotic Applications

The determination of the 6D singularity locus of the general Gough-Stewart platform is discussed in this article. The derivation of the velocity equation and the corresponding Jacobian matrices is first presented. Then a new procedure is introduced to obtain the analytical expression of the singularity locus, which is a function of six variables (x,y,z,ϕ,θ,ψ), using the velocity equation. Examples are also given to illustrate the results obtained. Gough-Stewart platforms can be used in several robotic applications as well as in flight simulators. The determination of the singularity locus is a very important design and application issue.

Preliminary results of numerical simulation of submarine landslide-generated waves

2021 ◽  
Author(s):  
Ramtin Sabeti ◽  
Mohammad Heidarzadeh
Keyword(s):  
Numerical Simulation ◽  
Numerical Modelling ◽  
Numerical Solutions ◽  
Numerical Technique ◽  
Source Region ◽  
Three Dimensional ◽  
Terminal Velocity ◽  
Sensitivity Analyses ◽  
Physical Experiments ◽  
Set Up

<p>Landslide-generated waves have been major threats to coastal areas and have led to destruction and casualties. Their importance is undisputed, most recently demonstrated by the 2018 Anak Krakatau tsunami, causing several hundred fatalities. The accurate prediction of the maximum initial amplitude of landslide waves (<em>η<sub>max</sub></em>) around the source region is a vital hazard indicator for coastal impact assessment. Laboratory experiments, analytical solutions and numerical modelling are three major methods to investigate the (<em>η<sub>max</sub></em>). However, the numerical modelling approach provides a more flexible and cost- and time-efficient tool. This research presents a numerical simulation of tsunamis due to rigid landslides with consideration of submerged conditions. In particular, this simulation focuses on studying the effect of landslide parameters on <em>η<sub>max</sub>.</em> Results of simulations are compared with our conducted physical experiments at the Brunel University London (UK) to validate the numerical model.</p><p>We employ the fully three-dimensional computational fluid dynamics package, FLOW-3D Hydro for modelling the landslide-generated waves. This software benefit from the Volume of Fluid Method (VOF) as the numerical technique for tracking and locating the free surface. The geometry of the simulation is set up according to the wave tank of physical experiments (i.e. 0.26 m wide, 0.50 m deep and 4.0 m). In order to calibrate the simulation model based on the laboratory measurements, the friction coefficient between solid block and incline is changed to 0.41; likewise, the terminal velocity of the landslide is set to 0.87 m/s. Good agreement between the numerical solutions and the experimental results is found. Sensitivity analyses of landslide parameters (e.g. slide volume, water depth, etc.) on <em>η<sub>max </sub></em>are performed. Dimensionless parameters are employed to study the sensitivity of the initial landslide waves to various landslide parameters.</p>

scholarly journals Design of a Passive Upper Limb Exoskeleton for Macaque Monkeys

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Junkai Lu ◽  
Kevin Haninger ◽  
Wenjie Chen ◽  
Suraj Gowda ◽  
Masayoshi Tomizuka ◽  
...  
Keyword(s):  
Upper Limb ◽  
Neural Control ◽  
Time Data ◽  
Upper Limb Exoskeleton ◽  
Contact Points ◽  
Shoulder Complex ◽  
Machine Interface ◽  
Set Up ◽  
Six Degree Of Freedom ◽  
Exoskeleton Design

Integrating an exoskeleton as the external apparatus for a brain–machine interface (BMI) has the advantage of providing multiple contact points to determine body segment postures and allowing control to and feedback from each joint. When using macaques as subjects to study the neural control of movement, an upper limb exoskeleton design with unlikely singularity is required to guarantee safe and accurate tracking of joint angles over all possible range of motion (ROM). Additionally, the compactness of the design is of more importance considering macaques have significantly smaller body dimensions than humans. This paper proposes a six degree-of-freedom (DOF) passive upper limb exoskeleton with 4DOFs at the shoulder complex. System kinematic analysis is investigated in terms of its singularity and manipulability. A real-time data acquisition system is set up, and system kinematic calibration is conducted. The effectiveness of the proposed exoskeleton system is finally demonstrated by a pilot animal test in the scenario of a reach and grasp task.

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