The Generation of Contact Surfaces of Indexing Cam Mechanisms—A Unified Approach

1994 ◽  
Vol 116 (2) ◽  
pp. 369-374 ◽  
Author(s):  
M. A. Gonza´lez-Palacios ◽  
J. Angeles
Keyword(s):  
Angular Velocity ◽  
Velocity Ratio ◽  
Rigid Bodies ◽  
Ruled Surfaces ◽  
Time Varying ◽  
Unified Approach ◽  
Unified Framework ◽  
Pressure Angle ◽  
Spatial Mechanisms ◽  
Contact Surfaces

In this paper the ruled surfaces of two rigid bodies that are in contact while moving with a prescribed time-varying angular-velocity ratio are generated. These are then used as the contact surfaces of indexing cam mechanisms. In this way, planar, spherical, and spatial mechanisms are synthesized in a unified framework, the pressure angle, for all these cases, being analyzed. The approach is illustrated with various examples.

The Generation of Contact Surfaces of Indexing Cam Mechanisms: A Unified Approach

1990 ◽  
Author(s):  
M. A. Gonzalez-Palacios ◽  
J. Angeles ◽  
Ch. Cai
Keyword(s):  
Angular Velocity ◽  
Velocity Ratio ◽  
Rigid Bodies ◽  
Ruled Surfaces ◽  
Time Varying ◽  
Unified Approach ◽  
Unified Framework ◽  
Spatial Mechanisms ◽  
Contact Surfaces

Abstract In this paper the ruled surfaces of two rigid bodies that are in contact while moving with a prescribed time-varying angular-velocity ratio are generated. These are then used as the contact surfaces of indexing cam mechanisms. In this way, planar, spherical and spatial mechanisms can be synthesized in a unified framework. The approach is illustrated with various examples.

scholarly journals Optimal Taylor–Couette turbulence

2012 ◽  
Vol 706 ◽  
pp. 118-149 ◽  
Author(s):  
Dennis P. M. van Gils ◽  
Sander G. Huisman ◽  
Siegfried Grossmann ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Angular Velocity ◽  
Probability Distribution Function ◽  
Neutral Line ◽  
Velocity Ratio ◽  
Outer Cylinder ◽  
Taylor Number ◽  
Counter Rotation ◽  
Taylor Couette

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

Analysis of Errors in the Double Hooke Joint

1965 ◽  
Vol 87 (2) ◽  
pp. 251-257 ◽  
Author(s):  
T. C. Austin ◽  
J. Denavit ◽  
R. S. Hartenberg
Keyword(s):  
Angular Velocity ◽  
Velocity Ratio ◽  
Displacement Velocity ◽  
Matrix Methods ◽  
Input And Output ◽  
Manufacturing Errors ◽  
Kinematic Analyses ◽  
Dimensional Errors ◽  
Analytical Expressions ◽  
The Ideal

A double Hooke joint consists of two properly connected single Hooke joints for the purpose of transmitting rotation with a uniform angular velocity ratio. Previous kinematic analyses [1, 2, 3] have dealt with Hooke joints of perfect or ideal configuration, viz., in which pertinent axes intersect and are perpendicular. With real Hooke joints the manufacturing errors (which include tolerances) produce axes that do not intersect and are not perpendicular. The present analysis [4] investigates the effects of such departures from the ideal for the case of the double Hooke joint. It considers their effect on the mechanism’s movability, and studies their influence on the displacement, velocity, and acceleration relations between input and output shafts. The problem is solved by matrix methods: displacement relations are derived for the ideal double Hooke joint, after which the effects of small dimensional errors are considered as perturbations from the ideal values. The analytical expressions allow the variations in velocities and accelerations to be obtained by differentiation.

On the Design of Planar and Spherical Pure-Rolling Indexing Cam Mechanisms

1992 ◽  
Author(s):  
Max Antonio González-Palacios ◽  
Jorge Angeles
Keyword(s):  
Coulomb Friction ◽  
Power Losses ◽  
Unified Framework ◽  
Pressure Angle ◽  
Pure Rolling

Abstract A new design of indexing cam mechanisms for parallel and intersecting shafts is presented here in a unified framework, so that both pure rolling and positive motion are achieved. Power losses due to Coulomb friction are eliminated, while producing motions free of jerk discontinuities. The pressure angle is anlyzed and applied to define the positive motion.

THE CALIBRATION OF AN ARRAY OF ACCELEROMETERS

2011 ◽  
Vol 35 (2) ◽  
pp. 251-267 ◽  
Author(s):  
Dany Dubé ◽  
Philippe Cardou
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Least Squares ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Rigid Bodies ◽  
New Method ◽  
Scale Factors ◽  
Array Calibration ◽  
The One

An accelerometer-array calibration method is proposed in this paper by which we estimate not only the accelerometer offsets and scale factors, but also their sensitive directions and positions on a rigid body. These latter parameters are computed from the classical equations that describe the kinematics of rigid bodies, and by measuring the accelerometer-array displacements using a magnetic sensor. Unlike calibration schemes that were reported before, the one proposed here guarantees that the estimated accelerometer-array parameters are globally optimum in the least-squares sense. The calibration procedure is tested on OCTA, a rigid body equipped with six biaxial accelerometers. It is demonstrated that the new method significantly reduces the errors when computing the angular velocity of a rigid body from the accelerometer measurements.

scholarly journals Solving a Problem of Rotary Motion for a Heavy Solid Using the Large Parameter Method

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
A. I. Ismail
Keyword(s):  
Angular Velocity ◽  
Small Parameter ◽  
Initial Conditions ◽  
Geometric Interpretation ◽  
Rigid Bodies ◽  
Parameter Method ◽  
Large Parameter ◽  
Small Parameter Method ◽  
Rotational Motions ◽  
The Stability

The small parameter method was applied for solving many rotational motions of heavy solids, rigid bodies, and gyroscopes for different problems which classify them according to certain initial conditions on moments of inertia and initial angular velocity components. For achieving the small parameter method, the authors have assumed that the initial angular velocity is sufficiently large. In this work, it is assumed that the initial angular velocity is sufficiently small to achieve the large parameter instead of the small one. In this manner, a lot of energy used for making the motion initially is saved. The obtained analytical periodic solutions are represented graphically using a computer program to show the geometric periodicity of the obtained solutions in some interval of time. In the end, the geometric interpretation of the stability of a motion is given.

The Mobility Equation and the Solvability of Joint Forces/Torques in Dynamic Analysis

1992 ◽  
Vol 114 (2) ◽  
pp. 257-262 ◽  
Author(s):  
Shin-Min Song ◽  
Xiaochun Gao
Keyword(s):  
Dynamic Analysis ◽  
Static Analysis ◽  
Rigid Bodies ◽  
Walking Machines ◽  
Spatial Mechanisms ◽  
Joint Forces ◽  
Simple Rules ◽  
Redundant Actuators

The mobility equation has been applied to predict the indeterminacy of unknown joint forces/torques in static analysis. In this paper, the mobility equation is modified to investigate the solvability of joint forces/torques of spatial mechanisms in dynamic analysis. Each factor which may contribute to indeterminacy is discussed and is explicitly expressed in the equation. With the modifications, the mobility equation can be applied to a system with or without redundant actuators. Together with the concept of subspaces and a few simple rules, the mobility equation can be used to identify the solvability of every joint unknown, as well as the equations which are required for the solutions, under the assumption of rigid bodies. This method can be used as a guidance of dynamic analysis in dealing with complicated systems such as walking machines and multi-fingered grippers.

A Unified Framework for Dynamics and Lyapunov Stability of Holonomically Constrained Rigid Bodies

2005 ◽  
Vol 9 (4) ◽  
pp. 387-394 ◽  
Author(s):  
Khoder Melhem ◽  
◽  
Zhaoheng Liu ◽  
Antonio Loría ◽  
◽  
...  
Keyword(s):  
System Dynamics ◽  
Lyapunov Stability ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Minimal Realization ◽  
State Variables ◽  
Unified Framework ◽  
Constrained System ◽  
And Control

A new dynamic model for interconnected rigid bodies is proposed here. The model formulation makes it possible to treat any physical system with finite number of degrees of freedom in a unified framework. This new model is a nonminimal realization of the system dynamics since it contains more state variables than is needed. A useful discussion shows how the dimension of the state of this model can be reduced by eliminating the redundancy in the equations of motion, thus obtaining the minimal realization of the system dynamics. With this formulation, we can for the first time explicitly determine the equations of the constraints between the elements of the mechanical system corresponding to the interconnected rigid bodies in question. One of the advantages coming with this model is that we can use it to demonstrate that Lyapunov stability and control structure for the constrained system can be deducted by projection in the submanifold of movement from appropriate Lyapunov stability and stabilizing control of the corresponding unconstrained system. This procedure is tested by some simulations using the model of two-link planar robot.

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