Planar Generalized Stewart Platforms and Their Direct Kinematics

2006 ◽  
pp. 198-211
Author(s):  
Gui-Fang Zhang ◽  
Xiao-Shan Gao
Keyword(s):  
Stewart Platforms ◽  
Direct Kinematics

A new method for solving the direct kinematics of general 6-6 Stewart Platforms using three linear extra sensors

2000 ◽  
Vol 35 (3) ◽  
pp. 423-436 ◽  
Author(s):  
Ilian A. Bonev ◽  
Jeha Ryu
Keyword(s):  
New Method ◽  
Stewart Platforms ◽  
Direct Kinematics

Direct Kinematics of General Stewart Platforms

1992 ◽  
Author(s):  
Anoop Dhingra ◽  
Dilip Kohli ◽  
Yong-Xian Xu
Keyword(s):  
Stewart Platform ◽  
Homotopy Method ◽  
Stewart Platforms ◽  
Direct Kinematics

Abstract A formulation for solving the direct kinematics of the general Stewart platform consisting of six moving and six grounded spheric joints is presented. The homotopy method is used for solving the direct kinematics of the platform, and it is shown that there exist a maximum of 40 possible solutions to the direct kinematics problem. These 40 solutions can be obtained by tracking only 64 homotopy paths. It is also shown that there are a maximum of 24 solutions for the Stewart platform with four spheric joints, and there exist a maximum of 16 solutions to the direct kinematics of the Stewart platform with three moving and three grounded spheric joints thus confirming the correctness of 24th and 16th degree direct kinematics polynomials obtained by other researchers.

scholarly journals Classification of direct kinematics to planar generalized Stewart platforms

2012 ◽  
Vol 45 (8) ◽  
pp. 458-473 ◽  
Author(s):  
Gui-Fang Zhang
Keyword(s):  
Stewart Platforms ◽  
Direct Kinematics

scholarly journals Strategies on Direct Kinematics to Generalized Stewart Platforms

2017 ◽  
Author(s):  
Gui-fang ZHANG ◽  
Jia-wen ZHANG ◽  
Li-na ZHAO
Keyword(s):  
Stewart Platforms ◽  
Direct Kinematics

scholarly journals Optimal layout and reconfiguration of a fixturing system constructed from passive Stewart platforms

2021 ◽  
Vol 60 ◽  
pp. 226-238
Author(s):  
Timotej Gašpar ◽  
Igor Kovač ◽  
Aleš Ude
Keyword(s):  
Optimal Layout ◽  
Stewart Platforms

scholarly journals On one approach to the approximation of solutions to the direct kinematics problem of parallel manipulators

2020 ◽  
Vol 10 (1) ◽  
pp. 65-70
Author(s):  
Andrei Gorchakov ◽  
Vyacheslav Mozolenko
Keyword(s):  
Neural Network ◽  
Bounded Function ◽  
Parallel Manipulators ◽  
Feedforward Neural Network ◽  
Numerical Implementation ◽  
Continuous Bounded Function ◽  
Space Filling ◽  
Space Filling Curves ◽  
Direct Kinematics

AbstractAny real continuous bounded function of many variables is representable as a superposition of functions of one variable and addition. Depending on the type of superposition, the requirements for the functions of one variable differ. The article investigated one of the options for the numerical implementation of such a superposition proposed by Sprecher. The superposition was presented as a three-layer Feedforward neural network, while the functions of the first’s layer were considered as a generator of space-filling curves (Peano curves). The resulting neural network was applied to the problems of direct kinematics of parallel manipulators.

Design and analysis of CICABOT: a novel translational parallel manipulator based on two 5-bar mechanisms

Robotica ◽  
2011 ◽  
Vol 30 (3) ◽  
pp. 449-456 ◽  
Author(s):  
M. F. Ruiz-Torres ◽  
E. Castillo-Castaneda ◽  
J. A. Briones-Leon
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Geometric Analysis ◽  
Vector Equation ◽  
Prismatic Joints ◽  
Hollow Cylinders ◽  
Moving Platform ◽  
Direct Kinematics

SUMMARYThis work presents the CICABOT, a novel 3-DOF translational parallel manipulator (TPM) with large workspace. The manipulator consists of two 5-bar mechanisms connected by two prismatic joints; the moving platform is on the union of these prismatic joints; each 5-bar mechanism has two legs. The mobility of the proposed mechanism, based on Gogu approach, is also presented. The inverse and direct kinematics are solved from geometric analysis. The manipulator's Jacobian is developed from the vector equation of the robot legs; the singularities can be easily derived from Jacobian matrix. The manipulator workspace is determined from analysis of a 5-bar mechanism; the resulting workspace is the intersection of two hollow cylinders that is much larger than other TPM with similar dimensions.

Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses

1994 ◽  
Vol 116 (2) ◽  
pp. 614-621 ◽  
Author(s):  
Yong-Xian Xu ◽  
D. Kohli ◽  
Tzu-Chen Weng
Keyword(s):  
Stability Index ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Static Force ◽  
Force Analysis ◽  
Kinematic Singularity ◽  
Numerical Examples ◽  
Transformation Matrices ◽  
Unstable Configuration ◽  
Direct Kinematics

A general formulation for the differential kinematics of hybrid-chain manipulators is developed based on transformation matrices. This formulation leads to velocity and acceleration analyses, as well as to the formation of Jacobians for singularity and unstable configuration analyses. A manipulator consisting of n nonsymmetrical subchains with an arbitrary arrangement of actuators in the subchain is called a hybrid-chain manipulator in this paper. The Jacobian of the manipulator (called here the system Jacobian) is a product of two matrices, namely the Jacobian of a leg and a matrix M containing the inverse of a matrix Dk, called the Jacobian of direct kinematics. The system Jacobian is singular when a leg Jacobian is singular; the resulting singularity is called the inverse kinematic singularity and it occurs at the boundary of inverse kinematic solutions. When the Dk matrix is singular, the M matrix and the system Jacobian do not exist. The singularity due to the singularity of the Dk matrix is the direct kinematic singularity and it provides positions where the manipulator as a whole loses at least one degree of freedom. Here the inputs to the manipulator become dependent on each other and are locked. While at these positions, the platform gains at least one degree of freedom, and becomes statically unstable. The system Jacobian may be used in the static force analysis. A stability index, defined in terms of the condition number of the Dk matrix, is proposed for evaluating the proximity of the configuration to the unstable configuration. Several illustrative numerical examples are presented.

Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator

2006 ◽  
Vol 129 (3) ◽  
pp. 320-325 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three-degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three-DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base mounted, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

Finding symmetric orthogonal Gough-Stewart platforms

2006 ◽  
Vol 22 (5) ◽  
pp. 880-889 ◽  
Author(s):  
J.E. McInroy ◽  
F. Jafari
Keyword(s):  
Stewart Platforms
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