scholarly journals Optimization of 3-DoF Manipulators’ Parasitic Motion with the Instantaneous Restriction Space-Based Analytic Coupling Relation

2021 ◽  
Vol 11 (10) ◽  
pp. 4690
Author(s):  
Hassen Nigatu ◽  
Doik Kim

This paper presents a velocity-level approach to optimizing the parasitic motion of 3-degrees of freedom (DoFs) parallel manipulators. To achieve this objective, we first systematically derive an analytical velocity-level parasitic motion equation as a primary step for the optimization. The paper utilizes an analytic structural constraint equation that describes the manipulator’s restriction space to formulate the parasitic motion equation via the task variable coupling relation. Then, the relevant geometric variables are identified from the analytic coupling equation. The Quasi-Newton method is used for the direction-specific minimization, i.e., optimizing either the x-axis or y-axis parasitic motion. The pattern-search algorithm is applied to optimize all parasitic terms from the workspace. The proposed approach equivalently describes the 3-PhRS, 3-PvRS, 3RPS manipulators. Moreover, other manipulators within a similar category can be equivalently expressed by the proposed method. Finally, the paper presents the resulting optimum configurations and numerical simulations to demonstrate the approach.

2021 ◽  
Author(s):  
Hassen Nigatu ◽  
Yun Ho Choi ◽  
Doik Kim

Abstract This paper presents a consistent analytic kinematic formulation of the 3-PRS parallel manipulator (PM) with a parasitic motion by embedding the velocity level structural constraint equation into the motion expression. Inverse rate kinematics (IRK) is solved with a simple constraint compatible velocity profile, which is obtained by projecting the instantaneous restriction space onto the motion space. Moreover, the systematic method to reveal the parasitic motion is introduced. Thus, the parasitic terms are automatically identified from the main motions. Unlike the usual approach, this study does not consider any explicit parasitic motion expression. Consequently, the derivation of constraint compatible input velocity, which comprises the parasitic term, is simplified. To incorporate the parasitic motion into the task velocity, constraint Jacobian of the manipulator is analytically obtained first. The manipulator Jacobian is extended to incorporate the passive joint’s information apart from the active joints and structural constraint. Hence, the dimension of the Jacobian matrix used to solve IRK is 9 × 6. The validity of the IRK is proved by the Bordered Gramian based forward rate kinematics (FRK). Then, an accurate numerical integration, RK4, is applied to the joint velocity of IRK to obtain the manipulator’s joint values. Consequently, the moving plate’s pose is obtained via forward position kinematics computed using integrated active and passive joint values for validation. The projection matrix used to get compatible constraint motion adjusts our input velocity and makes it compatible with the structural constraint policy, and the parasitic motion is embedded easily. Thus, an explicit formulation of the parasitic motion equation is not required, as the usual practice. Finally, the study presented numerical simulations to show the validity of the outlined resolutions. This paper’s result and analysis can be uniformly applied to other parallel manipulators with less than 6 DoFs.


Author(s):  
Saioa Herrero ◽  
Charles Pinto ◽  
Oscar Altuzarra ◽  
Constantino Roldan-Paraponiaris

Parallel manipulators, compared to serial manipulators, have some interesting properties, such as high stiffness, low inertia, high velocity, good accuracy and large payload capacity. Thus, parallel manipulators, especially the ones with one translation and two rotations as outputs (1T2R), are being increasingly studied. The 3PRS mechanism is a very typical example of this category, but it has accuracy problems caused by the parasitic motion, and low orientation capability. To overcome these problems, new mechanisms are being studied, such as the 2PRU-1PRS manipulator. As the 3PRS manipulator, the degrees of freedom of the 2PRU-1PRS are one translation along the Z-axis and two rotations about the X- and Y-axes. The advantages are that the parasitic motion appears only in one direction instead of in three and that the orientation capability is higher. In this paper we present the design of a 2PRU-1PRS mechanism suitable for vibration tests. In order to do this, we develop a code with an intuitive GUI (graphical user interface) that, for given variable limits, solves the inverse kinematic and dynamic problem for all the variable combinations and obtains the combination that consumes less power for an harmonic trajectory. Taking the simulations results into account, we propose a design that fulfils all the requirements for vibration tests in the three axes.


2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong ◽  
James Ritchie

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.


2021 ◽  
Author(s):  
Amin Moosavian

The ability to vary the geometry of a wing to adapt to different flight conditions can significantly improve the performance of an aircraft. However, the realization of any morphing concept will typically be accompanied by major challenges. Specifically, the geometrical constraints that are imposed by the shape of the wing and the magnitude of the air and inertia loads make the usage of conventional mechanisms inefficient for morphing applications. Such restrictions have served as inspirations for the design of a modular morphing concept, referred to as the Variable Geometry Wing-box (VGW). The design for the VGW is based on a novel class of reconfigurable robots referred to as Parallel Robots with Enhanced Stiffness (PRES) which are presented in this dissertation. The underlying feature of these robots is the efficient exploitation of redundancies in parallel manipulators. There have been three categories identified in the literature to classify redundancies in parallel manipulators: 1) actuation redundancy, 2) kinematic redundancy, and 3) sensor redundancy. A fourth category is introduced here, referred to as 4) static redundancy. The latter entails several advantages traditionally associated only with actuation redundancy, most significant of which is enhanced stiffness and static characteristics, without any form of actuation redundancy. Additionally, the PRES uses the available redundancies to 1) control more Degrees of Freedom (DOFs) than there are actuators in the system, that is, under-actuate, and 2) provide multiple degrees of fault tolerance. Although the majority of the presented work has been tailored to accommodate the VGW, it can be applied to any comparable system, where enhanced stiffness or static characteristics may be desired without actuation redundancy. In addition to the kinematic and the kinetostatic analyses of the PRES, which are developed and presented in this dissertation along with several case-studies, an optimal motion control algorithm for minimum energy actuation is proposed. Furthermore, the optimal configuration design for the VGW is studied. The optimal configuration design problem is posed in two parts: 1) the optimal limb configuration, and 2) the optimal topological configuration. The former seeks the optimal design of the kinematic joints and links, while the latter seeks the minimal compliance solution to their placement within the design space. In addition to the static and kinematic criteria required for reconfigurability, practical design considerations such as fail-safe requirements and design for minimal aeroelastic impact have been included as constraints in the optimization process. The effectiveness of the proposed design, analysis, and optimization is demonstrated through simulation and a multi-module reconfigurable prototype.


2012 ◽  
Vol 445 ◽  
pp. 917-922 ◽  
Author(s):  
Saman Davoodi ◽  
Amir Mostafapour

Leak detection is one of the most important problems in the oil and gas pipelines. Where it can lead to financial losses, severe human and environmental impacts. Acoustic emission test is a new technique for leak detection. Leakage in high pressure pipes creates stress waves resulting from localized loss of energy. Stress waves are transmitted through the pipe wall which will be recorded by using acoustic sensor or accelerometer installed on the pipe wall. Knowledge of how the pipe wall vibrates by acoustic emission resulting from leakage is a key parameter for leak detection and location. In this paper, modeling of pipe vibration caused by acoustic emission generated by escaping of fluid has been done. Donnells non linear theory for cylindrical shell is used to deriving of motion equation and simply supported boundary condition is considered. By using Galerkin method, the motion equation has been solved and a system of non linear equations with 6 degrees of freedom is obtained. To solve these equations, ODE tool of MATLAB software and Rung-Kuta numerical method is used and pipe wall radial displacement is obtained. For verification of this theory, acoustic emission test with continues leak source has been done. Vibration of wall pipe was recorded by using acoustic emission sensors. For better analysis, Fast Fourier Transform (FFT) was taken from theoretical and experimental results. By comparing the results, it is found that the range of frequencies which carried the most amount of energy is same which expresses the affectivity of the model.


1995 ◽  
Vol 117 (4) ◽  
pp. 658-661 ◽  
Author(s):  
H. R. Mohammadi Daniali ◽  
P. J. Zsombor-Murray ◽  
J. Angeles

Two versions of spatial double-triangular mechanisms are introduced, one with three and one with six degrees of freedom. Using dual-number quaternion algebra, a formula for the direct kinematics of these manipulators is derived. Numerical examples are included.


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