New Resolution Scheme of the Forward Kinematics of Parallel Manipulators Using Extra Sensors

1996 ◽  
Vol 118 (2) ◽  
pp. 214-219 ◽  
Author(s):  
Kilryong Han ◽  
Wankyun Chung ◽  
Y. Youm
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Parallel Manipulators ◽  
Stewart Platform ◽  
Forward Kinematics ◽  
Numerical Examples ◽  
Resolution Scheme ◽  
Real Time Applications ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

This paper presents a new closed-form resolution scheme of the forward kinematics of parallel manipulators based on two concepts, local structurization and mechanism partition. This scheme is applied to 6-DOF Stewart platform manipulators and the effectiveness of this scheme is verified through numerical examples. It is shown that one extra sensor is sufficient for both 3-3 SPM and 6-3 SPM to exactly resolve the forward kinematic problem (FKP) in closed form and two sensors for 6-6 SPM. In previous research, at least three extra sensors were needed for closed-form resolution of the FKP for 6-6 SPM. Consequently, the new resolution scheme is efficient to implement and easy for real-time applications for the control of parallel manipulators.

A new serial approach of the forward kinematic model of spherical parallel manipulators for real-time applications

2017 ◽  
Vol 232 (4) ◽  
pp. 677-684 ◽  
Author(s):  
Houssem Saafi ◽  
Margot Vulliez ◽  
Said Zeghloul ◽  
Med Amine Laribi
Keyword(s):  
Real Time ◽  
Model Calculation ◽  
Computing Time ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Parallel Structures ◽  
Kinematic Models ◽  
Real Time Applications ◽  
Critical Singularity ◽  
Forward Kinematic

Parallel architectures are increasingly used as haptic devices to provide low inertia, high stiffness and compactness. Thus, spherical parallel manipulators have been developed to generate the three rotational movements in a sufficient workspace. However, these parallel structures have complex kinematic models and can suffer from critical singularity issues. This paper proposes a serial approach to solve the forward kinematic model of a spherical parallel manipulator, which is used as a haptic device in minimally invasive surgery. The new forward kinematic model is based on the serial positioning of the three sensors on one leg rather than placing the three sensors on the three actuated base joints. The forward kinematic model calculation is thus simplified to be suitable for real-time applications (computing time around 5 µs) without cost increase. Parallel singularity effects are removed using this approach and the accuracy of the forward kinematic model is highly enhanced. Simulations were carried out to show the benefits of this approach. The resulting errors of the forward kinematic model calculation due to measurement noises do not exceed 0.2° along the workspace. Experiments were carried out to demonstrate the control of a surgical robot.

Economic Capital Modeling Closed Form Approximation for Real-Time Applications

2014 ◽  
Author(s):  
Thomas Ribarits ◽  
Axel Clement ◽  
Heikki Sepppll ◽  
Hua Bai ◽  
Ser-Huang Poon
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Economic Capital ◽  
Real Time Applications ◽  
Closed Form Approximation

Gröbner basis and resultant method for the forward displacement of 3-DoF planar parallel manipulators in seven-dimensional kinematic space

Robotica ◽  
2015 ◽  
Vol 34 (11) ◽  
pp. 2610-2628 ◽  
Author(s):  
Davood Naderi ◽  
Mehdi Tale-Masouleh ◽  
Payam Varshovi-Jaghargh
Keyword(s):  
Euclidean Space ◽  
Gröbner Basis ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dimensional Euclidean Space ◽  
Grobner Basis ◽  
Kinematic Space ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

SUMMARYIn this paper, the forward kinematic analysis of 3-degree-of-freedom planar parallel robots with identical limb structures is presented. The proposed algorithm is based on Study's kinematic mapping (E. Study, “von den Bewegungen und Umlegungen,” Math. Ann.39, 441–565 (1891)), resultant method, and the Gröbner basis in seven-dimensional kinematic space. The obtained solution in seven-dimensional kinematic space of the forward kinematic problem is mapped into three-dimensional Euclidean space. An alternative solution of the forward kinematic problem is obtained using resultant method in three-dimensional Euclidean space, and the result is compared with the obtained mapping result from seven-dimensional kinematic space. Both approaches lead to the same maximum number of solutions: 2, 6, 6, 6, 2, 2, 2, 6, 2, and 2 for the forward kinematic problem of planar parallel robots; 3-RPR, 3-RPR, 3-RRR, 3-RRR, 3-RRP, 3-RPP, 3-RPP, 3-PRR, 3-PRR, and 3-PRP, respectively.

Real-Time Forward Kinematics of the General 6-6 Stewart Platform Using One Extra Sensor

2000 ◽  
Author(s):  
Tae-Young Lee ◽  
Jae-Kyung Shim
Keyword(s):  
Real Time ◽  
Stewart Platform ◽  
Forward Kinematics ◽  
Double Precision ◽  
Leg Length ◽  
Precision Data ◽  
Constrained System ◽  
C Language ◽  
Estimates Of Solutions ◽  
Actual Configuration

Abstract The forward kinematics of the Stewart platform is to find the postures of the moving platform for a given set of leg lengths. In case of the general Stewart platform, the number of solutions of the problem is up to forty in the complex domain. Theoretically, it is not possible to uniquely determine the actual configuration with six leg length measurements only. An approach to get a single actual configuration is to make over-constrained system by adding extra sensors. This paper presents an algebraic elimination-based method for the real-time forward kinematics of the general Stewart platform with one extra sensor. The proposed algorithm does not require initial estimates of solutions unlike the numerical iterative methods, and can be implemented in C language using conventional double precision data with 15 significant digits. A numerical example is given to confirm the effectiveness and correctness of the developed algorithm for real-time computation.

A Novel Parallel Mechanism With 3-RRUR Legs

2007 ◽  
Author(s):  
Yanwen Li ◽  
Yueyue Zhang ◽  
Lumin Wang ◽  
Zhen Huang
Keyword(s):  
Machine Tools ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Symmetrical Structure ◽  
Forward Kinematic ◽  
Accumulated Error

This paper investigates a novel 4-DOF 3-RRUR parallel manipulator, the number and the characteristics of its degrees of freedom are determined firstly, the rational input plan and the invert and forward kinematic solutions are carried out then. The corresponding numeral example of the forward kinematics is given. This type of parallel manipulators has a symmetrical structure, less accumulated error, and can be used to construct virtual-axis machine tools. The analysis in this paper will play an important role in promoting the application of such manipulators.

Forward Kinematics of Nonpolyhedral Parallel Manipulators

1993 ◽  
Vol 115 (4) ◽  
pp. 938-940 ◽  
Author(s):  
Jean-Pierre Merlet
Keyword(s):  
Symmetry Axis ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Forward Kinematic

Forward kinematics has been studied for polyhedral parallel manipulators. We present here an algorithm for the forward kinematic of nonpolyhedral manipulators the plates of which have a symmetry axis. We show that there will be at most 352 possible solutions and exhibit a configuration with eight solutions.

Forward Kinematics Solution Distribution and Analytic Singularity-Free Workspace of Linear-Actuated Symmetrical Spherical Parallel Manipulators

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal Seneviratne
Keyword(s):  
Coordinate System ◽  
Optimization Design ◽  
Parallel Manipulators ◽  
Geometric Constraints ◽  
Forward Kinematics ◽  
Kinematics Model ◽  
Analytic Singularity ◽  
Dynamics And Control ◽  
Rotation Motion ◽  
Forward Kinematic

This paper presents a new kinematics model for linear-actuated symmetrical spherical parallel manipulators (LASSPMs) which are commonly used considering their symmetrical kinematics and dynamics properties. The model has significant advantages in solving the forward kinematic equations, and in analytically obtaining singularity loci and the singularity-free workspace. The Cayley formula, including the three Rodriguez–Hamilton parameters from a general rotation matrix, is provided and used in describing the rotation motion and geometric constraints of LASSPMs. Analytical solutions of the forward kinematic equations are obtained. Then singularity loci are derived, and represented in a new coordinate system with the three Rodriguez–Hamilton parameters assigned in three perpendicular directions. Limb-actuation singularity loci are illustrated and forward kinematics (FK) solution distribution in the singularity-free zones is discussed. Based on this analysis, unique forward kinematic solutions of LASSPMs can be determined. By using Cayley formula, analytical workspace boundaries are expressed, based on a given mechanism structure and input actuation limits. The singularity-free workspace is demonstrated in the proposed coordinate system. The work gives a systematic method in modeling kinematics, singularity and workspace analysis which provides new optimization design index and a simpler kinematics model for dynamics and control of LASSPMs.

scholarly journals Real-Time Inverse Kinematics of the Human Arm

1996 ◽  
Vol 5 (4) ◽  
pp. 393-401 ◽  
Author(s):  
Deepak Tolani ◽  
Norman I. Badler
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Upper Bound ◽  
Multiple Solutions ◽  
Inverse Kinematics ◽  
Additional Constraint ◽  
Degree Of Freedom ◽  
Empirical Results ◽  
Human Arm ◽  
Real Time Applications

A simple inverse kinematics procedure is proposed for a seven degree of freedom model of the human arm. Two schemes are used to provide an additional constraint leading to closed-form analytical equations with an upper bound of two or four solutions, Multiple solutions can be evaluated on the basis of their proximity from the rest angles or the previous configuration of the arm. Empirical results demonstrate that the procedure is well suited for real-time applications.

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