Dead Center Identification of Two-Degrees-of-Freedom Planar Parallel Manipulator Using Graph Theory and Transmission Angle

2020 ◽  
Vol 12 (5) ◽  
Author(s):  
Liangyi Nie ◽  
Huafeng Ding
Keyword(s):  
Graph Theory ◽  
Degrees Of Freedom ◽  
Fundamental Problem ◽  
Parallel Manipulators ◽  
Design Stage ◽  
Two Degrees Of Freedom ◽  
Operation Speed ◽  
Transmission Angle ◽  
The Dead ◽  
Independent Loops

Abstract Parallel manipulators are widely applied for their advantages of high stiffness, load-bearing, operation speed, and precision positioning capabilities, which are required in many industrial applications. However, dead center identification is a challenging task and fundamental problem during design stage of parallel manipulators, and becomes more intractable for two-degrees-of-freedom (DOF) complex planar parallel manipulators (PPMs) design. This paper proposes a method to identify the dead center positions of two-DOF PPMs based on graph theory and transmission angle. First, these PPMs are denoted by a set of independent loops using a topological structural analysis of the kinematic chains and structural decomposition. Then, the relationship between the mobility factor and the loop factor in the same independent loop is utilized to obtain the folded or stretched operation to form the new PPMs containing the corresponding instantaneous virtual loop. Subsequently, the dead center positions can be located since the corresponding transmission angle of the new PPMs is equal to 0 deg or 180 deg. As a result, the solved dead center positions of the two-DOF three types seven-bar, nine-bar, and 11-bar PPMs will provide guidance for the proper design of these PPMs. Finally, the Jacobian method for identifying the dead center position is then used to verify the proposed method. The proposed method is systematic and programmable and can be applied to any two-DOF PPM regardless of the number of independent loops or types of joints.

Motion Performance Analysis of Double-Cylinder Parallel Manipulators

2009 ◽  
Author(s):  
Hong Zhou ◽  
Shehu T. Alimi ◽  
Aravind Ravindranath ◽  
Hareesh Vepuri
Keyword(s):  
Performance Analysis ◽  
Parallel Manipulator ◽  
Critical Role ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Serial Manipulators ◽  
Operation Speed ◽  
Transmission Angle ◽  
Motion Performance ◽  
Two Degree Of Freedom

Double-cylinder parallel manipulators are closed-loop two-degree-of-freedom linkages. They are preferred to use because of their simplicity plus the common advantages of parallel manipulators such as high stiffness, load-bearing, operation speed and precision positioning. Like other parallel manipulators, the output motion of double-cylinder parallel manipulators is not as flexible as two-degree-of-freedom serial manipulators. The motion performance analysis plays a critical role for this type of parallel manipulator to be applied successfully. In this paper, the linkage feasibility conditions are established based on the transmission angle. When feasibility conditions are satisfied, there is no dead position during operation. The workspace is generated by using curve-enveloping theory. The singularity characteristics are analyzed within the workspace. The motion performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. The results of this paper provide guidelines to apply this type of parallel manipulator.

An Innovative Approach to Detect Isomorphism in Planar and Geared Kinematic Chains Using Graph Theory

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Vinjamuri Venkata Kamesh ◽  
Kuchibhotla Mallikarjuna Rao ◽  
Annambhotla Balaji Srinivasa Rao
Keyword(s):  
Graph Theory ◽  
Degrees Of Freedom ◽  
Quantitative Measure ◽  
Simple Algorithm ◽  
Isomorphism Problem ◽  
Innovative Approach ◽  
Two Degrees Of Freedom ◽  
Kinematic Chains ◽  
Topological Characteristics ◽  
Interesting Area

Detection of isomorphism in planar and geared kinematic chains (GKCs) is an interesting area since many years. Enumeration of planar and geared kinematic chains becomes easy only when isomorphism problem is resolved effectively. Many researchers proposed algorithms based on topological characteristics or some coding which need lot of computations and comparisons. In this paper, a novel and simple algorithm is proposed based on graph theory by which elimination of isomorphic chains can be done very easily without any tedious calculations or comparisons. A new concept “Net distance” is proposed based on the graph theory to be a quantitative measure to assess isomorphism in planar kinematic chains (PKCs) as well as GKCs. The proposed algorithm is applied on nine-link two-degrees-of-freedom (DOF) distinct kinematic chains completely and the results are presented. Algorithm is tested on examples from eight-link 1-DOF, ten-link 1-DOF, 12-link 1-DOF, and 15link 4-DOF PKCs. The algorithm is also tested on four-, six-link 1-DOF GKCs to detect isomorphism. All the results are in agreement with the existing literature.

Conceptual Design of Lower-Mobility Parallel Manipulators Based on Wrench Graphs

2014 ◽  
Author(s):  
Gamal El-Ghazaly ◽  
Stéphane Caro
Keyword(s):  
Degrees Of Freedom ◽  
A Priori ◽  
Three Dimensional ◽  
Main Idea ◽  
Parallel Manipulators ◽  
Geometric Constraints ◽  
Design Stage ◽  
Case Scenario ◽  
Worst Case ◽  
Lower Mobility

This paper presents a design methodology for lower-mobility parallel manipulators based on classification of wrench systems into four main classes. Wrench systems are represented in a three-dimensional projective space ℙ3 using wrench graphs where it is easy to incorporate geometric constraints to have simple singularity conditions using Grassmann-Cayley algebra (GCA). The main idea of the approach is to design a PM with an overall (constraint and actuation) wrench system that complies with a given wrench graph for which singularity conditions have been predetermined. The main advantage of this methodology is that the singularity conditions are already known a priori and consequently, it gives an opportunity to avoid such conditions at the design stage and make them unreachable. In the worst case scenario, where none of singularity conditions cannot be avoided, one can have a PM with known singular configurations which are always difficult to determine for already designed manipulators. As illustrative examples, two different five degrees-of-freedom (dof) mechanisms have been designed based on some of the defined wrench graphs giving 3T2R motion pattern. The first mechanism has some avoided singularities and the second one is free of singularity.

Motion Performance Analysis of Double-Slider Two-DOF Parallel Manipulators

2010 ◽  
Author(s):  
Hong Zhou ◽  
Mukesh Nagapuri ◽  
Sheetal Reddy Mamidi ◽  
Raj Kumar Gandham
Keyword(s):  
Performance Analysis ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Serial Manipulators ◽  
Operation Speed ◽  
Transmission Angle ◽  
Motion Performance ◽  
The Common ◽  
Two Degree Of Freedom

Double-slider parallel manipulators are closed-loop two-degree-of-freedom linkages. They are preferred to use because of their simplicity plus the common advantages of parallel manipulators such as high stiffness, load-bearing, operation speed and precision positioning. Like other parallel manipulators, the output motion of double-slider parallel manipulators is not as flexible as two-degree-of-freedom serial manipulators. The motion performance analysis plays a crucial role for this type of parallel manipulator to be applied successfully. In this paper, the linkage feasibility conditions are established based on the transmission angle. When feasibility conditions are satisfied, there is no dead position during operation. The workspace is generated by using curve-enveloping theory. The singularity characteristics are analyzed within the workspace. The motion performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. The results of this paper provide guidelines to design this type of parallel manipulator.

The scientific bases of autocontrol with vibration phase for a resonance beating-vibration system with two degrees of freedom driven by debalances

1996 ◽  
Vol 18 (2) ◽  
pp. 43-48
Author(s):  
Tran Van Tuan ◽  
Do Sanh ◽  
Luu Duc Thach
Keyword(s):  
Degrees Of Freedom ◽  
Regulation System ◽  
Vibration System ◽  
Two Degrees Of Freedom ◽  
System Operating

In the paper it is introduced a method for studying dynamics of beating-vibrators by means of digital calculation with the help of the machine in accordance with the needs by the helps of an available auto regulation system operating with high reability.

scholarly journals Two Degrees of Freedom Slip Controller with Lateral Torque Distribution

2020 ◽  
Vol 53 (2) ◽  
pp. 14450-14455
Author(s):  
Wolfgang Degel ◽  
Stefan Lupberger ◽  
Dirk Odenthal ◽  
Naim Bajcinca
Keyword(s):  
Degrees Of Freedom ◽  
Torque Distribution ◽  
Two Degrees Of Freedom

scholarly journals Torque Ripple Suppression of PMSM Based on Robust Two Degrees-of-Freedom Resonant Controller

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1015
Author(s):  
Mingfei Huang ◽  
Yongting Deng ◽  
Hongwen Li ◽  
Jing Liu ◽  
Meng Shao ◽  
...  
Keyword(s):  
Control Strategy ◽  
Measurement Errors ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Torque Ripple ◽  
Current Loop ◽  
Two Degrees Of Freedom ◽  
Robust Stability Analysis ◽  
Resonant Controller ◽  
Testing Environments

This paper concentrates on a robust resonant control strategy of a permanent magnet synchronous motor (PMSM) for electric drivers with model uncertainties and external disturbances to improve the control performance of the current loop. Firstly, to reduce the torque ripple of PMSM, the resonant controller with fractional order (FO) calculus is introduced. Then, a robust two degrees-of-freedom (Robust-TDOF) control strategy was designed based on the modified resonant controller. Finally, by combining the two control methods, this study proposes an enhanced Robust-TDOF regulation method, named as the robust two degrees-of-freedom resonant controller (Robust-TDOFR), to guarantee the robustness of model uncertainty and to further improve the performance with minimized periodic torque ripples. Meanwhile, a tuning method was constructed followed by stability and robust stability analysis. Furthermore, the proposed Robust-TDOFR control method was applied in the current loop of a PMSM to suppress the periodic current harmonics caused by non-ideal factors of inverter and current measurement errors. Finally, simulations and experiments were performed to validate our control strategy. The simulation and experimental results showed that the THDs (total harmonic distortion) of phase current decreased to a level of 0.69% and 5.79% in the two testing environments.

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