scholarly journals A Study on the Effect of the Contact Point and the Contact Force of a Glass Fiber under End-Face Polishing Process

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Ying-Chien Tsai ◽  
Guang-Miao Huang ◽  
Shin-Wei Cheng ◽  
Cheng-An Hsu ◽  
Innchyn Her
Keyword(s):  
Mathematical Model ◽  
Glass Fiber ◽  
Contact Force ◽  
Contact Point ◽  
Coupling Efficiency ◽  
Single Mode ◽  
Contact Forces ◽  
Initial Contact ◽  
Fiber Core ◽  
The Mathematical Model

The offset between the center lines of the polished end-face and the fiber core has a significant effect on coupling efficiency. The initial contact point and the contact force are two of the most important parameters that induce the offset. This study proposes an image assistant method to find the initial contact point and a mathematical model to estimate the contact force when fabricating the double-variable-curvature end-face of single mode glass fiber. The repeatability of finding the initial contact point via the vision assistant program is 0.3 μm. Based on the assumption of a large deflection, a mathematical model is developed to study the relationship between the contact force and the displacement of the lapping film. In order to verify the feasibility of the mathematical model, experiments, as well as DEFORM simulations, are carried out. The results show that the contact forces are alomst linearly proportional to the feed amounts of the lapping film and the errors are less than 9%. By using the method developed in this study, the offset between the grinding end-face and the center line of the fiber core is within 0.15 to 0.35 μm.

Choosing the Optimal Contact Force Distribution for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
Normal Vector ◽  
Optimization Criteria ◽  
Contact Force Distribution

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The optimal solution is found using a two-step approach: first finding the description of the entire solution space for the contact force distribution for a statically stable stance under friction constraints, and then choosing an optimal solution in this solution space which maximizes the objectives given by the chosen optimization criteria. An incremental strategy of opening up the friction cones is developed to produce the optimal solution which is defined as the one whose foot contact force vector is closest to the surface normal vector for robustness against slipping. The procedure is aided by using the “force space graph” which indicates where this solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point for the case when one foot is more critical than the other. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

Analysis and Visualization of the Contact Force Solution Space for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Solution Process ◽  
Solution Space ◽  
Contact Forces ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Force Components ◽  
The Relationship

A new analytical method for determining, describing, and visualizing the solution space for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The foot contact forces are first resolved into strategically defined foot contact force components to decouple them for simplifying the solution process, and then the static equilibrium equations are applied to find certain contact force components and the relationship between the others. Using the friction cone equation at each foot contact point and the known contact force components, the problem is transformed into a geometrical one to find the ranges of contact forces and the relationship between them that satisfy the friction constraint. Using geometric properties of the friction cones and by simple manipulation of their conic sections, the whole solution space which satisfies the static equilibrium and friction constraints at each contact point can be found. Two representation schemes, the “force space graph” and the “solution volume representation,” are developed for describing and visualizing the solution space which gives an intuitive visual map of how well the solution space is formed for the given conditions of the system.

Motion of a Sphere on a Plane

1994 ◽  
Author(s):  
Yong-Xian Xu ◽  
Dilip Kohli ◽  
Larry Vezina ◽  
Daniel R. Speranza
Keyword(s):  
Mathematical Model ◽  
Initial Conditions ◽  
Contact Point ◽  
Break Point ◽  
Degree Of Freedom ◽  
Geometric Center ◽  
Inertia Properties ◽  
Gyroscopic Motion ◽  
The Mathematical Model ◽  
First Time

Abstract The motion of a sphere on a plane is a five degree-of-freedom motion. It consists of two independent translations of the geometric center of the sphere and three rotations corresponding to gyroscopic motion of the sphere. The trajectory of an imbalanced sphere on the plane depends on: (1) the physical and inertia properties of the sphere, (2) the initial conditions of motion, and (3) the friction between the sphere and the plane. To predict the trajectory of the sphere, a general Eulerian mathematical model is developed which takes into account these conditions. The mathematical model is verified through experimentation. For the first time, general characteristics of the translatory and rotatory motions of the imbalanced sphere with general inertia distribution are presented. The existence of the “break point” in the trajectory is illustrated by examples. The trajectory (track) of the contact point on the surface of the sphere is also analyzed.

Optimal Contact Force Distribution for Multi-Limbed Robots

2005 ◽  
Vol 128 (3) ◽  
pp. 566-573 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Three Dimensional ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
New Strategy ◽  
Contact Force Distribution

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The incremental strategy of opening up the friction cones is aided by using the “force space graph” which indicates where the solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

Visualization of the Contact Force Solution Space for Multi-Limbed Robots

2005 ◽  
Vol 128 (1) ◽  
pp. 295-302 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Three Dimensional ◽  
Solution Space ◽  
Entire Solution ◽  
Contact Forces ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Force Components

A new analytical method for determining, describing, and visualizing the solution space for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The foot contact forces are first resolved into strategically defined foot contact force components to decouple them, and then the static equilibrium equations are applied. Using the friction cone equation at each foot contact point, the problem is then transformed into a geometrical one. Using geometric properties of the friction cones and by simple manipulation of their conic sections, the entire solution space which satisfies the static equilibrium and friction constraints at each contact point can be found. Two representation schemes, the “force space graph” and the “solution volume representation,” are developed for describing and visualizing the solution space which gives an intuitive visual map of how well the solution space is formed for the given conditions of the system.

Nonintrusive Measurement of Contact Forces During Vibration Dominated Impacts

2004 ◽  
Vol 126 (3) ◽  
pp. 489-497 ◽  
Author(s):  
Satwinder Jit Singh ◽  
Anindya Chatterjee
Keyword(s):  
Contact Force ◽  
Tikhonov Regularization ◽  
Strain Gauge ◽  
Initial Conditions ◽  
Contact Point ◽  
Electrical Contact ◽  
Contact Forces ◽  
Force Estimation ◽  
Contact Duration ◽  
Gauge Data

Impact force estimation is done indirectly through, e.g., strain measurements away from the contact point, because inserting a force transducer between the contacting objects changes the force. Most prior contact force measurements involved a single contact interval. Here we study transverse impacts of a slender beam and a clamped-free plate; contact occurs more than once within one impact. Strain gauge data, electrical contact detection, and a dynamic model of the beam are used to estimate the contact force. The problem of force estimation from strain gauge data is ill-posed, and Tikhonov regularization fails initially. A reduced-order model is then developed using symmetry, and better initial conditions are estimated using a Kalman filter. Subsequently, Tikhonov regularization gives excellent force estimates, empirically supported by the contact duration measurements. Two other methods that explicitly use the contact duration measurements are also given. The first uses Tikhonov regularization within each contact interval, followed by Kalman filtering during noncontact to get initial conditions for the next contact. The second uses truncated Fourier sine series in each contact interval and is, computationally, the simplest. All three methods provide consistent force estimates. Our work complements recent work by Inoue and coworkers where the impulse response of the colliding object was measured separately using a Hopkinson bar, and electrical contact was not monitored.

Contact Status Optimization of Multibody Dynamic Systems Using Dual Variable Transformation

2014 ◽  
Author(s):  
Carlotta Mummolo ◽  
Luigi Mangialardi ◽  
Joo H. Kim
Keyword(s):  
Contact Force ◽  
Dynamic Systems ◽  
Contact Point ◽  
A Priori ◽  
Iterative Solution ◽  
Contact Forces ◽  
Analytical Relationship ◽  
Sqp Algorithm ◽  
Predictive Algorithm ◽  
Classical Formulation

Generating the motion of redundant systems under general constraints within an optimization framework is a problem not yet solved, as there is, so far, a lack of completely predictive methods that concurrently solve for the optimal trajectory and the contact status induced by the given constraints. A novel approach for optimal motion planning of multibody systems with contacts is developed, based on a Sequential Quadratic Programming (SQP) algorithm for Nonlinear Programming (NLP). The objective is to detect and optimize the contact status and the relative contact force within the optimization sequential problem, while simultaneously optimizing a trajectory. The novelty is to seek for the contact information within the iterative solution of the SQP algorithm and use this information to sequentially update the resulting contact force in the system’s dynamic model. This is possible by looking at the analytical relationship between the dual variables resulting from the constrained NLP and the Lagrange multipliers that represent the contact forces in the classical formulation of constrained dynamic systems. This approach will result in a fully predictive algorithm that doesn’t require any a priori knowledge on the contact status (e.g., time of contact, point of contact, etc.) or contact force magnitude. A preliminary formulation is presented, as well as numerical experiments on simple planar manipulators, as demonstration of concepts.

Modeling and Dynamic Analysis of an Electrical Helmholtz Resonator for Active Control of Resonant Noise

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Sang-Myeong Kim ◽  
Joao A. Pereira ◽  
Antonio E. Turra ◽  
Jun-Ho Cho
Keyword(s):  
Mathematical Model ◽  
Dynamic Control ◽  
Active Noise Control ◽  
Helmholtz Resonator ◽  
Single Mode ◽  
Band Pass Filter ◽  
Pass Filter ◽  
Acoustic Cavity ◽  
Resonant Noise ◽  
The Mathematical Model

This paper describes a theoretical and experimental investigation into an electrical Helmholtz resonator (EHR): that is, an active noise control (ANC) loudspeaker used in conjunction with a microphone and a feedback controller for suppressing resonant noise in an acoustic cavity. The microphone is collocated with the loudspeaker and a band pass filter of second-order is used as the control filter inside the controller. The EHR is configured as such in order to suppress an acoustic mode that is within the volume velocity drive frequency range of the loudspeaker used. The concepts of impedance and passivity are used to develop the mathematical model as well as to study its dynamics. From these, it is theoretically shown that the EHR for single-mode suppression is an extremely low-impedance acoustic damping device that electrically realizes the pressure neutralization mechanism of a conventional Helmholtz resonator (HR). Experimental work is also presented, in which an EHR is constructed to suppress the Helmholtz mode of an acoustic cavity at about 40 Hz by more than 40 dB, to justify the mathematical model and also to verify the dynamic control mechanism.

scholarly journals Regular Mechanical Transformation of Rotations Into Translations: Part 1. Kinematic Analysis and Definition of the Basic Characteristics

2017 ◽  
Vol 47 (2) ◽  
pp. 3-23
Author(s):  
Emilia Abadjieva ◽  
Valentin Abadjiev
Keyword(s):  
Mathematical Model ◽  
Contact Point ◽  
Sliding Velocity ◽  
Mechanical Transformation ◽  
Basic Characteristics ◽  
Definition Of ◽  
Object Of Study ◽  
The Mathematical Model ◽  
Geometric Primitives ◽  
Regular Transformation

Abstract The science that study the processes of motions transformation upon a preliminary defined law between non-coplanar axes (in general case) axes of rotations or axis of rotation and direction of rectilinear translation by three-link mechanisms, equipped with high kinematic joints, can be treated as an independent branch of Applied Mechanics. It deals with mechanical behaviour of these multibody systems in relation to the kinematic and geometric characteristics of the elements of the high kinematic joints, which form them. The object of study here is the process of regular transformation of rotation into translation. The developed mathematical model is subjected to the defined task for studying the sliding velocity vector function at the contact point from the surfaces elements of arbitrary high kinematic joints. The main kinematic characteristics of the studied type motions transformation (kinematic cylinders on level, kinematic relative helices (helical conoids) and kinematic pitch configurations) are defined on the bases of the realized analysis. These features expand the theoretical knowledge, which is the objective of the gearing theory. They also complement the system of kinematic and geometric primitives, that form the mathematical model for synthesis of spatial rack mechanisms.

scholarly journals Non-smooth dynamic modeling and simulation of an unmanned bicycle on a curved pavement

2022 ◽  
Vol 43 (1) ◽  
pp. 93-112
Author(s):  
Kaiming Zhang ◽  
Xudong Zheng ◽  
Zhang Chen ◽  
Bin Liang ◽  
Tianshu Wang ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Friction Force ◽  
Contact Force ◽  
Contact Point ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Force Model ◽  
Lagrange Equations ◽  
Stick Slip ◽  
Normal Contact

AbstractThe non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground. According to the Carvallo-Whipple configuration, the unmanned bicycle is reduced to four rigid bodies, namely, rear wheel, rear frame, front fork, and front wheel, which are connected by perfect revolute joints. The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point, and these forces are described by the Hunt-Crossley contact force model and the LuGre friction force model, respectively. According to the characteristics of flat and curved pavements, calculation methods for contact forces and their generalized forces are presented. The dynamics of the system is modeled by the Lagrange equations of the first kind, a numerical solution algorithm of the dynamic equations is presented, and the Baumgarte stabilization method is used to restrict the drift of the constraints. The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies. The feasibility of the proposed model is demonstrated by simulations under different motion states.

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