Closed Form Solution to Workspace of Hexapod-Based Virtual Axis Machine Tools

1999 ◽  
Vol 121 (1) ◽  
pp. 26-31 ◽  
Author(s):  
T. Huang ◽  
J. Wang ◽  
D. J. Whitehouse
Keyword(s):  
Machine Tools ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mobile Platform ◽  
Unified Framework ◽  
Closed Solution ◽  
Workspace Analysis ◽  
Position And Orientation ◽  
First Time ◽  
Workspace Boundary

A novel methodology is presented in this paper for the workspace analysis of virtual axis machine tools. The workspace is defined which enables to describe in a unified framework both the position and orientation capabilities of the mobile platform. Given a range of the orientation of the mobile platform, the piecewise closed solution to the workspace boundary is formulated. It is indicated for the first time that the workspace boundary in fact is the cap of twelve envelope surfaces. Two examples are given to illustrate the effectiveness of this approach.

Determination of Closed Form Solution to the Workspace of Stewart Parallel Manipulators

1998 ◽  
Author(s):  
T. Huang ◽  
J. S. Wang ◽  
J. X. Yuan
Keyword(s):  
Closed Form Solution ◽  
Parallel Manipulators ◽  
Form Solution ◽  
Mobile Platform ◽  
Unified Framework ◽  
Spherical Curve ◽  
Spherical Surfaces ◽  
Workspace Analysis ◽  
Yaw Angle ◽  
Workspace Boundary

Abstract A novel methodology is presented in this paper for the workspace analysis of Stewart parallel manipulators. The workspace is defined in such a way that enables a description to be made in a unified framework of both the position and orientation capabilities of the mobile platform. Given the orientation capability of the mobile platform which is described by the minimum reachable yaw angle, the piecewise closed solution to the position workspace boundary is formulated by means of differential geometry. It is indicated that the workspace boundary is in fact the cap of twelve envelope surfaces, each of which is generated by a family of spherical surfaces with the center moving along a two branch closed spherical curve. Two examples are given to illustrate the effectiveness of this approach.

scholarly journals Nonlocal Elasticity Response of Doubly-Curved Nanoshells

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 466 ◽  
Author(s):  
Mohammad Hassan Dindarloo ◽  
Li Li ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Nonlocal Parameter ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Theory Of Elasticity ◽  
Form Solution ◽  
Small Scale ◽  
Unified Framework ◽  
Geometrical Properties ◽  
Small Scale Effect ◽  
Doubly Curved

In this paper, we focus on the bending behavior of isotropic doubly-curved nanoshells based on a high-order shear deformation theory, whose shape functions are selected as an accurate combination of exponential and trigonometric functions instead of the classical polynomial functions. The small-scale effect of the nanostructure is modeled according to the differential law consequent, but is not equivalent to the strain-driven nonlocal integral theory of elasticity equipped with Helmholtz’s averaging kernel. The governing equations of the problem are obtained from the Hamilton’s principle, whereas the Navier’s series are proposed for a closed form solution of the structural problem involving simply-supported nanostructures. The work provides a unified framework for the bending study of both thin and thick symmetric doubly-curved shallow and deep nanoshells, while investigating spherical and cylindrical panels subjected to a point or a sinusoidal loading condition. The effect of several parameters, such as the nonlocal parameter, as well as the mechanical and geometrical properties, is investigated on the bending deflection of isotropic doubly-curved shallow and deep nanoshells. The numerical results from our investigation could be considered as valid benchmarks in the literature for possible further analyses of doubly-curved applications in nanotechnology.

A Method for Determining and Correcting Robot Position and Orientation Errors Due to Manufacturing

1988 ◽  
Vol 110 (1) ◽  
pp. 3-10 ◽  
Author(s):  
P. L. Broderick ◽  
R. J. Cipra
Keyword(s):  
Closed Form Solution ◽  
Difficult Problem ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Correct Position ◽  
Forward Solution ◽  
Simple Task ◽  
Position And Orientation ◽  
Robot Position ◽  
Kinematic Solution

A method is presented for calibration of a robot to correct position and orientation errors due to manufacturing. The method is based on the shape matrix robot kinematic description. Each joint is individually and successively moved in order to explicitly calculate the shape matrix of each link. In addition, methods to correct for the errors in both the forward and inverse kinematic solutions are presented. The modification of the forward solution is a simple task. The modification of the inverse kinematic solution is a difficult problem and is achieved by an iterative technique which supplements the closed-form solution. An example of the calibration and inverse solution is presented to show the improvement in the accuracy of the robot.

scholarly journals Decoupled Closed-Form Solution for Humanoid Lower Limb Kinematics

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Alejandro Said ◽  
Ernesto Rodriguez-Leal ◽  
Rogelio Soto ◽  
J. L. Gordillo ◽  
Leonardo Garrido
Keyword(s):  
Closed Form ◽  
Lower Limb ◽  
Closed Form Solution ◽  
Numerical Data ◽  
Geometric Approach ◽  
Form Solution ◽  
Experimental Implementation ◽  
Limb Kinematics ◽  
Position And Orientation ◽  
Lower Limb Kinematics

This paper presents an explicit, omnidirectional, analytical, and decoupled closed-form solution for the lower limb kinematics of the humanoid robot NAO. The paper starts by decoupling the position and orientation analysis from the overall Denavit-Hartenberg (DH) transformation matrices. Here, the joint activation sequence for the DH matrices is based on the geometry of a triangle. Furthermore, the implementation of a forward and a reversed kinematic analysis for the support and swing phase equations is developed to avoid matrix inversion. The allocation of constant transformations allows the position and orientation end-coordinate systems to be aligned with each other. Also, the redefinition of the DH transformations and the use of constraints allow decoupling the shared DOF between the legs and the torso. Finally, a geometric approach to avoid the singularities during the walking process is indicated. Numerical data is presented along with an experimental implementation to prove the validity of the analytical results.

scholarly journals New Application of the(G′/G)-Expansion Method for Thin Film Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Wafaa M. Taha ◽  
M. S. M. Noorani ◽  
I. Hashim
Keyword(s):  
Thin Film ◽  
Traveling Wave ◽  
Closed Form Solution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Form Solution ◽  
Thin Film Equations ◽  
First Time ◽  
Positive Integers ◽  
Good Agreement

The(G′/G)-expansion method is used for the first time to find traveling wave solutions for thin film equations, where it is found that the related balance numbers are not the usual positive integers. The closed-form solution obtained via this method is in good agreement with the previously obtained solutions of other researchers. It is also noted that, for appropriate parameters, new solitary waves solutions are found.

scholarly journals Closed-Form Solution to the Position Analysis of Watt–Baranov Trusses Using the Bilateration Method

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Nicolás Rojas ◽  
Federico Thomas
Keyword(s):  
Closed Form ◽  
Characteristic Polynomial ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations ◽  
Characteristic Polynomials ◽  
Position Analysis ◽  
Exact Position ◽  
Kinematic Loops ◽  
First Time

The exact position analysis of a planar mechanism reduces to compute the roots of its characteristic polynomial. Obtaining this polynomial almost invariably involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. The use of kinematic loops to this end has seldom been questioned despite deriving the characteristic polynomial from them requires complex variable eliminations and, in most cases, trigonometric substitutions. As an alternative, the bilateration method has recently been used to obtain the characteristic polynomials of the three-loop Baranov trusses without relying on variable eliminations nor trigonometric substitutions and using no other tools than elementary algebra. This paper shows how this technique can be applied to members of a family of Baranov trusses resulting from the circular concatenation of the Watt mechanism irrespective of the resulting number of kinematic loops. To our knowledge, this is the first time that the characteristic polynomial of a Baranov truss with more that five loops has been obtained, and hence, its position analysis solved in closed form.

A PLATE MODEL FOR THE EVALUATION OF PULL-IN INSTABILITY OCCURRENCE IN ELECTROSTATIC MICROPUMP DIAPHRAGMS

2011 ◽  
Vol 03 (01) ◽  
pp. 1-19 ◽  
Author(s):  
EMANUELE BERTARELLI ◽  
RAFFAELE ARDITO ◽  
RAFFAELE ARDITO ◽  
ALBERTO CORIGLIANO ◽  
ROBERTO CONTRO
Keyword(s):  
Nonlinear Dynamics ◽  
Loading Condition ◽  
Mechanical Response ◽  
Closed Form Solution ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Plate Model ◽  
The One ◽  
Quality Factor Q ◽  
First Time

This work deals with the mechanical response of circular microplates undergoing electrostatic actuation. A one degree-of-freedom model and Finite Element approaches are exploited in a nondimensional framework. First, a quasi-static conventional approach is adopted. From the one degree-of-freedom model a closed form solution for the plate electromechanical problem is obtained for the first time. Then a strong attention is paid to pull-in phenomena in nonlinear dynamics. Dynamic behavior of the structure is explored, leading to the identification of a pull-in loading condition which is dependent on the quality factor Q. The outcomes are discussed and widely compared with those available in the literature for similar microsystems.

scholarly journals Closed-Form Solution of a Peripherally Fixed Circular Membrane under Uniformly Distributed Transverse Loads and Deflection Restrictions

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Teng-fei Wang ◽  
Xiao-ting He ◽  
Yang-hui Li
Keyword(s):  
Approximate Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Axisymmetric Deformation ◽  
Form Solution ◽  
Circular Membrane ◽  
Rigid Plate ◽  
Membrane Stress ◽  
Transverse Loads ◽  
First Time

The problem of axisymmetric deformation of a peripherally fixed and uniformly loaded circular membrane under deflection restrictions (by a frictionless horizontal rigid plate) was analytically solved, where the assumption of constant membrane stress adopted in the existing work was given up, and a closed-form solution of this problem was presented for the first time. The numerical analysis shows that the closed-form solution presented here has higher calculation accuracy than the existing approximate solution.

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