Analytical form solution of the direct kinematics of a 4–4 fully in-parallel actuated six degree-of-freedom mechanism

2005 ◽  
pp. 41-50
Author(s):  
C. Innocenti ◽  
V. Parenti-Castelli
Keyword(s):  
Analytical Form ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Six Degree Of Freedom ◽  
Direct Kinematics

scholarly journals Kinematic analysis of the 3-RPS-3-SPR series–parallel manipulator

Robotica ◽  
2018 ◽  
Vol 37 (7) ◽  
pp. 1240-1266 ◽  
Author(s):  
Abhilash Nayak ◽  
Stéphane Caro ◽  
Philippe Wenger
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
End Effector ◽  
Inverse Kinematics Problem ◽  
Univariate Polynomial ◽  
Six Degree Of Freedom ◽  
Independent Parameters ◽  
Direct Kinematics

SUMMARYThis paper deals with the kinematic analysis and enumeration of singularities of the six degree-of-freedom 3-RPS-3-SPR series–parallel manipulator (S–PM). The characteristic tetrahedron of the S–PM is established, whose degeneracy is bijectively mapped to the serial singularities of the S–PM. Study parametrization is used to determine six independent parameters that characterize the S–PM and the direct kinematics problem is solved by mapping the transformation matrix between the base and the end-effector to a point in ℙ7. The inverse kinematics problem of the 3-RPS-3-SPR S–PM amounts to find the location of three points on three lines. This problem leads to a minimal octic univariate polynomial with four quadratic factors.

Manipulator Configurations Based on Rotary-Linear (R-L) Actuators and Their Direct and Inverse Kinematics

1988 ◽  
Vol 110 (4) ◽  
pp. 397-404 ◽  
Author(s):  
D. Kohli ◽  
Soo-Hun Lee ◽  
Kao-Yueh Tsai ◽  
G. N. Sandor
Keyword(s):  
Inverse Kinematics ◽  
Polynomial Equation ◽  
Open Loop ◽  
Degree Of Freedom ◽  
Serial Link ◽  
New Type ◽  
Computationally Intensive ◽  
Six Degree Of Freedom ◽  
Two Degree Of Freedom ◽  
Direct Kinematics

In this paper, a new type of two-degree-of-freedom actuator called the rotary-linear (R-L) actuator is described. The R-L actuator permits a rotation and a translation along the axis of rotation, thus simulating a cylinder pair. The R-L actuators are then used in type synthesis of mechanical manipulator chains. Closed-loop three-, four, five, and six-degree-of-freedom chains containing four to nine links, R-L actuators, revolute pairs (R), prismatic pairs (P), cylindrical pairs (C), and spheric pairs (S) are then obtained. A class of manipulator configurations where the hand is connected to the ground via six-degree-of-freedom dyads or triads and containing three grounded R-L actuators is treated for inverse kinematics. Since all the actuators are on the ground in this configuration, higher payload capacities and smaller actuator sizes can be expected from these configurations. In addition, generally, the computations required for inverse kinematics are also significantly less than those required for serial link open-loop manipulators. The direct kinematics, however, is much more involved and computationally intensive for these manipulators than for serial-link manipulators. The direct kinematics of an example manipulator is derived and requires solution of a 16th-order polynomial equation. Numerical examples are presented for illustration.

Iterative feedback control based on frequency response model for a six-degree-of-freedom micro-vibration platform

2021 ◽  
pp. 107754632199731
Author(s):  
He Zhu ◽  
Shuai He ◽  
Zhenbang Xu ◽  
XiaoMing Wang ◽  
Chao Qin ◽  
...  
Keyword(s):  
Feedback Control ◽  
Frequency Response ◽  
Control Strategy ◽  
Degree Of Freedom ◽  
Small Displacement ◽  
Response Model ◽  
Parameter Uncertainties ◽  
Micro Vibration ◽  
Six Degree Of Freedom ◽  
Iterative Feedback

In this article, a six-degree-of-freedom (6-DOF) micro-vibration platform (6-MVP) based on the Gough–Stewart configuration is designed to reproduce the 6-DOF micro-vibration that occurs at the installation surfaces of sensitive space-based instruments such as large space optical loads and laser communications equipment. The platform’s dynamic model is simplified because of the small displacement characteristics of micro-vibrations. By considering the multifrequency line spectrum characteristics of micro-vibrations and the parameter uncertainties, an iterative feedback control strategy based on a frequency response model is designed, and the effectiveness of the proposed control strategy is verified by performing integrated simulations. Finally, micro-vibration experiments are performed with a 10 kg load on the platform. The results of these micro-vibration experiments show that after several iterations, the amplitude control errors are less than 3% and the phase control errors are less than 1°. The control strategy presented in this article offers the advantages of a simple algorithm and high precision and it can also be used to control other similar micro-vibration platforms.

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