A General Approach to the Large Deflection Problems of Spatial Flexible Rods Using Principal Axes Decomposition of Compliance Matrices

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Genliang Chen ◽  
Zhuang Zhang ◽  
Hao Wang
Keyword(s):  
Degrees Of Freedom ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Closed Form Solution ◽  
Form Solution ◽  
Robot Kinematics ◽  
Flexible Rods ◽  
Equilibrium Configurations ◽  
Principal Axes ◽  
Compliance Matrices

This paper presents a general discretization-based approach to the large deflection problems of spatial flexible links in compliant mechanisms. Based on the principal axes decomposition of structural compliance matrices, a particular type of elements, which relate to spatial six degrees-of-freedom (DOF) serial mechanisms with passive elastic joints, is developed to characterize the force-deflection behavior of the discretized small segments. Hence, the large deflection problems of spatial flexible rods can be transformed to the determination of static equilibrium configurations of their equivalent hyper-redundant mechanisms. The main advantage of the proposed method comes from the use of robot kinematics/statics, rather than structural mechanics. Thus, a closed-form solution to the system overall stiffness can be derived straightforwardly for efficient gradient-based searching algorithms. Two kinds of typical equilibrium problems are intensively discussed and the correctness has been verified by means of physical experiments. In addition, a 2DOF planar compliant parallel manipulator is provided as a case study to demonstrate the potential applications.

Toward a Minimal Dynamic Model of a 6-DOF Parallel Robot

1997 ◽  
Author(s):  
L. Beji ◽  
M. Pascal ◽  
P. Joli
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Parallel Robot ◽  
Form Solution ◽  
Lagrangian Formalism ◽  
Inverse Kinematic Problem ◽  
Geometrical Properties

Abstract In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.

scholarly journals Control of Three Degrees-of-Freedom Wave Energy Converters Using Pseudo-Spectral Methods

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Ossama Abdelkhalik ◽  
Shangyan Zou ◽  
Rush Robinett ◽  
Giorgio Bacelli ◽  
David Wilson ◽  
...  
Keyword(s):  
Optimal Control ◽  
Wave Energy ◽  
Parametric Excitation ◽  
Degrees Of Freedom ◽  
Closed Form Solution ◽  
Form Solution ◽  
Programming Approach ◽  
Wave Energy Converters ◽  
Pseudo Spectral ◽  
Three Degrees Of Freedom

Abstract This paper presents a solution to the optimal control problem of a three degrees-of-freedom (3DOF) wave energy converter (WEC). The three modes are the heave, pitch, and surge. The dynamic model is characterized by a coupling between the pitch and surge modes, while the heave is decoupled. The heave, however, excites the pitch motion through nonlinear parametric excitation in the pitch mode. This paper uses Fourier series (FS) as basis functions to approximate the states and the control. A simplified model is first used where the parametric excitation term is neglected and a closed-form solution for the optimal control is developed. For the parametrically excited case, a sequential quadratic programming approach is implemented to solve for the optimal control numerically. Numerical results show that the harvested energy from three modes is greater than three times the harvested energy from the heave mode alone. Moreover, the harvested energy using a control that accounts for the parametric excitation is significantly higher than the energy harvested when neglecting this nonlinear parametric excitation term.

Simulation and Optimization of Flexible Hooke Hinge

2012 ◽  
Vol 201-202 ◽  
pp. 574-577 ◽  
Author(s):  
Wei Sun
Keyword(s):  
Degrees Of Freedom ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Rotation Angle ◽  
Basic Unit ◽  
Excellent Performance ◽  
Simulation And Optimization ◽  
Element Simulation ◽  
New Type ◽  
Perpendicular Axis

Flexible Flexible hinge is a typical flexible element in compliant mechanisms. Hooke hinge is a combination of the two revolute whose axis through the same point. It allows the two components have relative rotation of two degrees of freedom along the perpendicular axis. The distributed multi-reeds and large-deflection flexible Hooke hinge with the curve reed as the basic unit is analysed by finite element simulation, and is optimized in Multi-objective. The Hooke hinge after optimization lines with the basic rotation characteristics of Hooke hinge. It can provide the larger two-dimensional rotating schedule.It’s unilateral rotation angle can up to ±11.9 °, and the center drift and input coupling of rotation is small. So this flexible Hooke hinge is a new type of large deformation flexible Hook hinge which have excellent performance.

Thermal stresses in a rotating, nonhomogeneous, anisotropic disk of varying thickness and density

1975 ◽  
Vol 10 (3) ◽  
pp. 137-142 ◽  
Author(s):  
G V Gurushankar
Keyword(s):  
Thermal Loading ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Rotating Disk ◽  
Form Solution ◽  
Annular Disk ◽  
Varying Thickness ◽  
Principal Axes ◽  
Rotationally Symmetric ◽  
Anisotropic Disk

Closed form solution is obtained for stresses in a rotationally symmetric, nonhomogeneous, anisotropic, annular disk of varying thickness and density, subjected to thermal loading. Analysis is presented for a particular type of anisotropy, namely Polar Orthotropy, in which axes of anisotropy coincide with the principal axes of stresses at each point in the disk. The variations of homogenity, density and thickness are assumed to be hyperbolic. Numerical results in the form of graphs presented show the effect of nonhomogenity, density and degree of orthotropy on the stress distribution in a disk subjected to constant and varying temperature gradients. Homogeneous, varying density anisotropic rotating disk of varying thickness forms a special case of the analysis.

Analytical Puncture Study of Circular Metal Plates

1980 ◽  
Vol 102 (3) ◽  
pp. 242-248 ◽  
Author(s):  
R. C. Shieh
Keyword(s):  
Large Deflection ◽  
Plate Thickness ◽  
Closed Form Solution ◽  
Analytical Techniques ◽  
Correlation Study ◽  
Form Solution ◽  
Punch Force ◽  
Perfectly Plastic ◽  
Static Responses ◽  
Metal Plates

An existing closed-form solution for large-deflection static responses of centrally loaded, rigid, perfectly plastic circular metal plates (with emphasis on steel plate cases) that are clamped (built-in) or simply supported at the edges is first modified to take into account the effects of elastic deformation and material strainhardening in an approximate manner. The modified theoretical solution is first shown to correlate very well with experimental results. Then it is applied in solving the quasi-static plate puncture problem in which the punch bar penetrates slowly into the plate. An analytical/experimental correlation study on punch force-deflection relationship and incipient plate puncture energy is made on newly obtained experimental data. Effects of variation of strainhardening parameter, boundary conditions and shear deformation on incipient puncture energy are studied, and plate puncture design curves are developed in the form of nondimensional incipient plate puncture energy as a function of punch diameter/plate thickness ratio for various values of punch diameter/plate diameter ratio. Application of these analytical techniques/design curves to the design of nuclear shipping cask plate components subject to regulatory puncture drop loading is also discussed.

Development of a new buffing robot manipulator for shoes

Robotica ◽  
2008 ◽  
Vol 26 (1) ◽  
pp. 55-62 ◽  
Author(s):  
Hyeung-Sik Choi ◽  
Gyu-Deuk Hwang ◽  
Sam-Sang You
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Closed Form Solution ◽  
Electronic System ◽  
Form Solution ◽  
Graphic User Interface ◽  
Test Results ◽  
C Language ◽  
Communication Program

SUMMARYThis paper presents analysis and experimental verifications of a new robot manipulator with five degrees of freedom developed for the buffing operation of shoes. First, the forward and inverse kinematics are analyzed. Next, an analytic closed-form solution is rigorously derived for the joint angles corresponding to the position and orientation of the end-effector in Cartesian coordinates. A control system, including input/output interfaces and the related electronic system, is designed for the control of the mechanical structure of the buffing robot. Then, peripheral systems integrated with the conveyer, transfer device, and fixture device are designed for the sequential buffing process of shoes. Also, a graphic user interface (GUI) program including the forward/inverse kinematics, control algorithm, and communication program to interact the robot with the peripheral systems is developed by using visual C++ language. A new flexible toolholder (FTH) is proposed to compensate for the excessive applied force between deburring tools and shoes. Finally, the test results are provided to demonstrate the effectiveness of the proposed scheme.

scholarly journals Axisymmetric Large Deflection Elastic Analysis of Hollow Annular Membranes under Transverse Uniform Loading

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1770
Author(s):  
Jun-Yi Sun ◽  
Qi Zhang ◽  
Xue Li ◽  
Xiao-Ting He
Keyword(s):  
Closed Form ◽  
Circular Plate ◽  
Large Deflection ◽  
Closed Form Solution ◽  
Circular Ring ◽  
Form Solution ◽  
Elastic Response ◽  
Geometrically Nonlinear ◽  
Closed Form Solutions ◽  
Annular Membrane

The anticipated use of a hollow linearly elastic annular membrane for designing elastic shells has provided an impetus for this paper to investigate the large deflection geometrically nonlinear phenomena of such a hollow linearly elastic annular membrane under transverse uniform loads. The so-called hollow annular membranes differ from the traditional annular membranes available in the literature only in that the former has the inner edge attached to a movable but weightless rigid concentric circular ring while the latter has the inner edge attached to a movable but weightless rigid concentric circular plate. The hollow annular membranes remove the transverse uniform loads distributed on “circular plate” due to the use of “circular ring” and result in a reduction in elastic response. In this paper, the large deflection geometrically nonlinear problem of an initially flat, peripherally fixed, linearly elastic, transversely uniformly loaded hollow annular membrane is formulated, the problem formulated is solved by using power series method, and its closed-form solution is presented for the first time. The convergence and effectiveness of the closed-form solution presented are investigated numerically. A comparison between closed-form solutions for hollow and traditional annular membranes under the same conditions is conducted, to reveal the difference in elastic response, as well as the influence of different closed-form solutions on the anticipated use for designing elastic shells.

scholarly journals A Parallel Manipulator with Planar Configurable Platform and Three End-Effectors

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Jesus H. Tinajero-Campos
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Closed Form Solution ◽  
Form Solution ◽  
Terminal Link ◽  
Planar Parallel Manipulator ◽  
End Effectors ◽  
Newton Homotopy

This work reports on the kinematic analysis of a planar parallel manipulator endowed with a configurable platform assembled with six terminal links serially connected by means of revolute joints. This topology allows the robot manipulator to dispose of three relative degrees of freedom owing to the mobility of an internal closed-loop chain. Therefore, the proposed robot manipulator can admit three end-effectors. The forward displacement analysis of the configurable planar parallel manipulator is easily achieved based on unknown coordinates denoting the pose of each terminal link. Thereafter, the analysis leads to twelve quadratic equations which are numerically solved by means of the Newton homotopy method. Furthermore, a closed-form solution is available for the inverse position analysis. On the contrary, the instantaneous kinematics of the robot manipulator is investigated by means of the theory of screws. Numerical examples are included with the purpose to illustrate the method of kinematic analysis.

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