Nonlinear Isolator Optimization Using RMS Cost Function

2004 ◽  
Author(s):  
A. Narimani ◽  
M. F. Golnaraghi
Keyword(s):  
Closed Form Solution ◽  
Optimization Method ◽  
Relative Displacement ◽  
Form Solution ◽  
Jump Phenomenon ◽  
Nonlinear Parameters ◽  
Strongly Nonlinear ◽  
Damping Characteristics ◽  
Stiffness And Damping ◽  
Boundary Limits

In this paper using a modified averaging method the frequency response of a general nonlinear isolator is obtained. Stiffness and damping characteristics are considered cubic functions of displacement and velocity through the isolator. Analytical results are compared with those obtained by numerical integration in order to validate the closed form solution for strongly nonlinear isolator. While increasing the nonlinearity in the system improves the response of the isolator, stability and jump avoidance conditions set boundary limits for the parameters. The effects of nonlinear parameters to avoid jump phenomenon are discussed in detail. The set of parameters where the system behaves regularly are found and the nonlinear isolator is optimized based on RMS optimization method. Using this method the RMS function of absolute acceleration of the sprung mass is minimized versus the RMS function of relative displacement.

Dynamic Reynolds equation for micropolar fluids and the analysis of plane inclined slider bearings with squeezing effect

2007 ◽  
Vol 221 (7) ◽  
pp. 823-829 ◽  
Author(s):  
N. B. Naduvinamani ◽  
G. B. Marali
Keyword(s):  
Reynolds Equation ◽  
Coupling Parameter ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Form Solution ◽  
Squeezing Effect ◽  
Micropolar Fluids ◽  
Slider Bearings ◽  
Damping Characteristics ◽  
Stiffness And Damping

The general dynamic Reynolds equation of sliding-squeezing surfaces with micro-polar fluids is derived for the assessment of dynamic characteristics of bearings with general film thickness. The detailed analysis is presented for the plane inclined slider bearings by using perturbation method. Two Reynolds-type equations corresponding to steady performance and perturbed characteristics are obtained. The closed form solution of these equations is obtained. The numerical computations of the results show that, the micropolar fluids provide an improved characteristics for both steady-state and the dynamic stiffness and damping characteristics. It is found that the maximum steady-load-carrying capacity is function of coupling parameter and is achieved at smaller values of profile parameter for larger values of the coupling parameter.

scholarly journals A Closed-Form Solution for Estimating the Accuracy of Circular Feature’ Pose for Object 2D-3D Pose Estimation System

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Cui Li ◽  
Derong Chen ◽  
Jiulu Gong ◽  
Yangyu Wu
Keyword(s):  
Closed Form ◽  
Covariance Matrix ◽  
Pose Estimation ◽  
Closed Form Solution ◽  
Optimization Method ◽  
Form Solution ◽  
Synthetic Image ◽  
Point Selection ◽  
3D Pose Estimation ◽  
Estimation System

Many objects in the real world have circular feature. In general, circular feature’s pose is represented by 5-DoF (degree of freedom) vector ξ = X , Y , Z , α , β T . It is a difficult task to measure the accuracy of circular feature’s pose in each direction and the correlation between each direction. This paper proposes a closed-form solution for estimating the accuracy of pose transformation of circular feature. The covariance matrix of ξ is used to measure the accuracy of the pose. The relationship between the pose of the circular feature of 3D object and the 2D points is analyzed to yield an implicit function, and then Gauss–Newton theorem is employed to compute the partial derivatives of the function with respect to such point, and after that the covariance matrix is computed from both the 2D points and the extraction error. In addition, the method utilizes the covariance matrix of 5-DoF circular feature’s pose variables to optimize the pose estimator. Based on pose covariance, minimize the mean square error (Min-MSE) metric is introduced to guide good 2D imaging point selection, and the total amount of noise introduced into the pose estimator can be reduced. This work provides an accuracy method for object 2D-3D pose estimation using circular feature. At last, the effectiveness of the method for estimating the accuracy is validated based on both random data sets and synthetic images. Various synthetic image sequences are illustrated to show the performance and advantages of the proposed pose optimization method for estimating circular feature’s pose.

Analysis and Optimal Synthesis of the RSCR Spatial Mechanism

1991 ◽  
Author(s):  
G. K. Ananthasuresh ◽  
Steven N. Kramer
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Optimization Method ◽  
Form Solution ◽  
Mechanism Analysis ◽  
Motion Generation ◽  
Spatial Mechanism ◽  
Geometric Characteristics ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints

Abstract The closed form solution of the analysis of the RSCR (Revolute-Spherical-Cylindrical-Revolute) spatial mechanism is presented in this paper. This work is based on the geometric characteristics of the mechanism involving the following three cases: the cone, the cylinder and the one-sheet hyperboloid. These cases derive their names from the nature of the locus of the slider of the linkage as viewed from the output side. Each case is then treated separately to develop a closed form, geometry based analysis technique. These analysis modules are then used to optimally synthesize the mechanism for function, path and motion generation problems satisfying precision conditions within prescribed accuracy limits. The Selective Precision Synthesis technique is employed to formulate the nonlinear inequality constraints. These constraints along with an objective function and other constraints are solved using the Generalized Reduced Gradient method of optimization. In addition, the use of mobility charts is used to aid the designer in making a judicious choice for the initial design point before invoking the optimization method. The determination of the transmission angle for the RSCR mechanism is also described and numerical examples for function, path and motion generation are also included. This new closed form method of analysis based on geometric characteristics is computationally less intensive than other available techniques for spatial mechanism analysis and helps in the visualization of the physical mechanism; something that is not possible with most vector and matrix methods.

scholarly journals Compliance of a microfibril subjected to shear and normal loads

2008 ◽  
Vol 5 (26) ◽  
pp. 1087-1097 ◽  
Author(s):  
Jingzhou Liu ◽  
Chung-Yuen Hui ◽  
Lulin Shen ◽  
Anand Jagota
Keyword(s):  
Nonlinear Response ◽  
Closed Form Solution ◽  
Elliptic Functions ◽  
Surface Region ◽  
Form Solution ◽  
Compliant Structure ◽  
Strongly Nonlinear ◽  
Indentation Experiment ◽  
Backing Layer ◽  
Nonlinear Deformations

Many synthetic bio-inspired adhesives consist of an array of microfibrils attached to an elastic backing layer, resulting in a tough and compliant structure. The surface region is usually subjected to large and nonlinear deformations during contact with an indenter, leading to a strongly nonlinear response. In order to understand the compliance of the fibrillar regions, we examine the nonlinear deformation of a single fibril subjected to a combination of shear and normal loads. An exact closed-form solution is obtained using elliptic functions. The prediction of our model compares well with the results of an indentation experiment.

scholarly journals Mobility analysis of a robotic cardiopulmonary resuscitation device

2021 ◽  
Author(s):  
Mahdi Ardestani ◽  
Mohsen Asgari
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Closed Form Solution ◽  
Parallel Manipulators ◽  
Optimization Method ◽  
Form Solution ◽  
Mobility Analysis ◽  
Chest Compressions ◽  
Singularity Problem ◽  
Lower Mobility

Abstract During chest compressions action, in CPR (CPR), the 2 arms of the rescuer constitute a parallel mechanism. Inspired by this performance, during this study a specific family of lower mobility parallel manipulators by employing a modified version of Delta robot is proposed for chest compressions in rescuing a patient. One of the biggest differences between this mechanism and the Delta parallel mechanism is that the position of the three active connections of the robot relative to each other has changed the geometry of the platforms. Also, it shapes the asymmetrical structure within the robot mechanism and its workspace. Another difference is due to the architectural optimization method considering the mixed performance index, which has been used during this mechanism to achieve a much better compromise between the manipulator dexterity and its workspace. Within the present paper, after introducing the architecture of the robot, a closed-form solution is developed for the kinematic problem and therefore the results are verified using MSC. Adams©. Then Jacobian matrix is generated to gauge the singularity problem of the proposed mechanism. then, the workspace of the robot is investigated and compared with the original Delta mechanism.

scholarly journals Use of a Strongly Nonlinear Gambier Equation for the Construction of Exact Closed Form Solutions of Nonlinear ODEs

2007 ◽  
Vol 2007 ◽  
pp. 1-25
Author(s):  
M. P. Markakis
Keyword(s):  
Closed Form ◽  
Initial Conditions ◽  
Closed Form Solution ◽  
Form Solution ◽  
Nonlinear Odes ◽  
Analytical Technique ◽  
Closed Form Solutions ◽  
Strongly Nonlinear ◽  
Parameter Values

We establish an analytical method leading to a more general form of the exact solution of a nonlinear ODE of the second order due to Gambier. The treatment is based on the introduction and determination of a new function, by means of which the solution of the original equation is expressed. This treatment is applied to another nonlinear equation, subjected to the same general class as that of Gambier, by constructing step by step an appropriate analytical technique. The developed procedure yields a general exact closed form solution of this equation, valid for specific values of the parameters involved and containing two arbitrary (free) parameters evaluated by the relevant initial conditions. We finally verify this technique by applying it to two specific sets of parameter values of the equation under consideration.

Gyroscopic and Support Effects on the Steady-State Response of a Noncontacting Flexibly Mounted Rotor Mechanical Face Seal

1989 ◽  
Vol 111 (2) ◽  
pp. 200-206 ◽  
Author(s):  
I. Green
Keyword(s):  
Dynamic Response ◽  
Closed Form Solution ◽  
Form Solution ◽  
Steady State Response ◽  
Face Seal ◽  
State Response ◽  
High Speeds ◽  
Relative Response ◽  
Mechanical Face Seal ◽  
Stiffness And Damping

The dynamic behavior of a noncontacting rotary mechanical face seal is analyzed. A closed-form solution is presented for the response of a flexibly mounted rotor to forcing misalignments which normally exist due to manufacturing and assembly tolerances. The relative misalignment between the rotor and the stator, which is the most important seal parameter, has been found to be time dependent with a cyclically varying magnitude. The relative response is minimum when support stiffness and damping are minimum. The gyroscopic couple is shown to have a direct effect on the dynamic response. This effect is enhanced at high speeds, and depending on the ratio between the transverse and polar moments of inertia, it can either decrease or increase the dynamic response. Its effect is most beneficial to seal performance when the rotor is a “short disk.” A numerical example demonstrates that a flexibly-mounted rotor seal outperforms a flexibly mounted stator seal with regard to the total relative misalignment, the critical stator misalignment, and the critical speed.

Analysis and Optimal Synthesis of the RSCR Spatial Mechanisms

1994 ◽  
Vol 116 (1) ◽  
pp. 174-181 ◽  
Author(s):  
G. K. Ananthasuresh ◽  
S. N. Kramer
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Optimization Method ◽  
Form Solution ◽  
Mechanism Analysis ◽  
Motion Generation ◽  
Spatial Mechanism ◽  
Geometric Characteristics ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints

A closed form solution of the analysis of the RSCR (Revolute-Spherical-Cylindrical-Revolute) spatial mechanism is presented in this paper. This work is based on the geometric characteristics of the mechanism involving the following three cases: the cone, the cylinder, and the one-sheet hyperboloid. These cases derive their names from the nature of the locus of the slider of the linkage as viewed from the output side. Each case is then treated separately to develop a closed form, geometry based analysis technique. These analysis modules are then used to optimally synthesize the mechanism for function, path and motion generation problems satisfying precision conditions within prescribed accuracy limits. The Selective Precision Synthesis technique is employed to formulate the nonlinear inequality constraints. These constraints along with an objective function and other constraints are solved using the Generalized Reduced Gradient method of optimization. In addition, mobility charts are used to aid the designer in making a judicious choice for the initial design point before invoking the optimization method. Numerical examples are presented to validate the theory. This new closed form method of analysis that is based on geometric characteristics is computationally less intensive than other available techniques for spatial mechanism analysis and helps in the visualization of the physical mechanism; something that is not possible with most vector and matrix methods.

scholarly journals Energy-saving optimization method for point-to-point trajectories planned via standard primitives in 1-DoF mechatronic systems

2021 ◽  
Author(s):  
Giovanni Carabin ◽  
Renato Vidoni
Keyword(s):  
Closed Form Solution ◽  
Optimization Method ◽  
Form Solution ◽  
Motor Drives ◽  
Mechatronic Systems ◽  
Analytical Methodology ◽  
Point Trajectories ◽  
Point To Point ◽  
Theoretical Results ◽  
Energy Formulation

AbstractIn this work, an analytical methodology to minimize the energy expenditure of mechatronic systems performing point-to-point (PTP) trajectories based on well-known motion primitives is developed and validated. Both PTP trajectory profiles commonly used in industrial motor drives and more complex ones are investigated. Focusing on generic 1-DoF mechatronic systems moving a constant inertia load (e.g., elevators, cranes, CNC machines, Cartesian axis) and possibly equipped or retrofitted with regenerative devices, the consumed energy formulation is firstly derived. Then, the analytical optimization considering all the selected PTP trajectory profiles is computed and a generic closed-form solution is determined. Finally, numerical and experimental evaluations are done showing the effectiveness of the theoretical results and proposed methodology. In addition, all the different trajectories are compared with respect to energy consumption.

Finite Kinematic Synthesis of a Cycloidal-Crank Mechanism for Function Generation

1970 ◽  
Vol 92 (3) ◽  
pp. 531-535 ◽  
Author(s):  
S. N. Kramer ◽  
G. N. Sandor
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Optimization Method ◽  
Gear Ratio ◽  
Form Solution ◽  
Complex Numbers ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Approximate Function ◽  
Crank Mechanism

The method of complex numbers is applied towards the kinematic synthesis of a planar geared five-bar cycloidal-crank mechanism for approximate function generation with finitely separated precision points. It is shown that up to 10 precision points can be obtained, and a closed-form solution is presented which yields up to 6 different mechanisms with a 6-point approximation. In this method, the designer has control over the design of the cycloidal crank regarding gear ratio and configuration. The method has been programmed for automatic digital computation on the IBM-360 system, and the program is made available to interested readers. An optimization method utilizing iterative application of the closed-form solution is outlined.

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