The Synthesis of Cam-Oscillating Roller-Follower Mechanisms: A Unified Approach

1992 ◽  
Author(s):  
Max Antonio González-Palacios ◽  
Jorge Angeles
Keyword(s):  
Differential Geometry ◽  
Contact Line ◽  
Contact Surface ◽  
Dual Numbers ◽  
Sliding Velocity ◽  
Unified Approach ◽  
Pressure Angle

Abstract A unified approach to the synthesis of the contact surface of cam-oscillating roller-follower mechanisms is presented. This is achieved using dual numbers. The surfaces of both cam and roller are obtained so that, at their contact line, a minimum-magnitude sliding velocity is produced. The differential geometry of the pitch surface and the pressure angle are both analyzed.

Synthesis of the Base Curves For N-Lobed Elliptical Gears

2004 ◽  
Vol 127 (5) ◽  
pp. 997-1005 ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Differential Geometry ◽  
Tooth Profile ◽  
Spur Gears ◽  
Profile Angle ◽  
Pressure Angle ◽  
Base Circle ◽  
Noncircular Gears ◽  
The Right ◽  
First Time ◽  
Envelope Theory

Motivated by the need to synthesize the tooth profiles of noncircular gears, we approach the synthesis of the tooth profile of circular spur gears using their pitch circle, rather than their base circle. We do this by means of envelope theory. The proposed formulation gives the involute tooth profile and its well-known base circle for any pitch radius and profile angle of the rack cutter, which coincides with the pressure angle for circular gears. Then, the foregoing approach applies to the synthesis of the base curves of noncircular gears with involute tooth profiles and of their rack. We do this by resorting to basic differential geometry using the Euler–Savary Theorem, rather than to envelope theory. In particular, the formulation of both base curves for the right and left involute tooth profiles is obtained, for the first time, for N-lobed elliptical gears and their rack through the formulation of the pitch curves and their evolutes. The proposed formulation is illustrated with numerical results.

Analytical Design of Cam-Type Angular-Motion Compensators

1977 ◽  
Vol 99 (2) ◽  
pp. 381-386 ◽  
Author(s):  
S. G. Dhande ◽  
G. N. Sandor
Keyword(s):  
Principal Curvature ◽  
Three Dimensional ◽  
Angular Motion ◽  
Maximum Pressure ◽  
Exact Equation ◽  
Unified Approach ◽  
Analytical Design ◽  
Pressure Angle ◽  
Cam Profile ◽  
Different Dimensions

In this paper, a unified approach is presented for the analytical design of cams used in various angular-motion compensators. These mechanisms can be classified as cam-modulated linkages. For a predetermined phase control between the two coupled shafts of the compensator, using this method one can find the exact equation of the cam profile, its principal curvature at the point of contact, expressions for the pressure angle and the transmission angles, and the condition for maximum pressure angle as well as the cutter wheel positions for generating the cam profile on an appropriate machine tool. The equations developed can be used effectively for analyzing the mechanical error due to tolerances on different dimensions of this cam-modulated linkage. The analysis of three-dimensional cam-type angular-motion compensators is also included.

Synthesis of Contact Surfaces of Spherical Cam-Oscillating Roller-Follower Mechanisms: A General Approach

1991 ◽  
Author(s):  
Max Antonio González-Palacios ◽  
Jorge Angeles
Keyword(s):  
Sliding Velocity ◽  
Surface Geometry ◽  
Pressure Angle ◽  
Synthesis Technique ◽  
Novel Method ◽  
Contact Surfaces ◽  
Conical Surfaces

Abstract A novel method of synthesis of the surface geometry of spherical cam-oscillating roller-follower mechanisms is introduced. The approach aims at zeroing the sliding velocity between the cam and the roller, their respective geometries being thus obtained as conical surfaces. The pressure angle is analyzed in detail. Specific results are presented for the application of this synthesis technique to indexing cam mechanisms.

scholarly journals Mathematics and Poetry • Unification, Unity, Union

Sci ◽  
2020 ◽  
Vol 2 (4) ◽  
pp. 84
Author(s):  
Florin Felix Nichita
Keyword(s):  
Differential Geometry ◽  
Baxter Equation ◽  
Dual Numbers ◽  
Euler’S Formula ◽  
Euler’S Identity

We consider a multitude of topics in mathematics where unification constructions play an important role: the Yang–Baxter equation and its modified version, Euler’s formula for dual numbers, means and their inequalities, topics in differential geometry, etc. It is interesting to observe that the idea of unification (unity and union) is also present in poetry. Moreover, Euler’s identity is a source of inspiration for the post-modern poets.

Forming Principle and Error Analysis of Ballscrew Manufactured by Cold Rolling

2010 ◽  
Vol 33 ◽  
pp. 445-449
Author(s):  
X.Q. Wang ◽  
F.K. Cui ◽  
X.J. He
Keyword(s):  
Differential Geometry ◽  
Error Analysis ◽  
Cold Rolling ◽  
Contact Line ◽  
Processing Method ◽  
Profile Error ◽  
Cold Forming ◽  
Generating Method ◽  
Error Generation

According to differential geometry and meshing theory, the cold forming principle of ballscrew is investigated, the meshing model, the contact line and theoretical errors of the ballscrew are constructed, the objective moving laws between roller and workpiece are revealed by analyzing the meshing model and the contact line, the processing method of cold-rolling is considered as the generating method which can lay the foundation for roller design by analyzing forming principle. The error generation causes are discovered and the solutions are given by analyzing the profile error and the error of the actual helix of the centrode of ball.

scholarly journals Modeling Sliding Friction of a Multiscale Wavy Surface over a Viscoelastic Foundation Taking into Account Adhesion

Lubricants ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 13 ◽  
Author(s):  
Yulia Makhovskaya
Keyword(s):  
Contact Problem ◽  
Friction Force ◽  
Contact Surface ◽  
Sliding Friction ◽  
Adhesion Force ◽  
Wavy Surface ◽  
Viscoelastic Foundation ◽  
Sliding Velocity ◽  
Scale Level ◽  
Dry Conditions

A model for calculating the hysteretic friction force for a multilevel wavy surface sliding in dry conditions over the surface of a viscoelastic foundation is suggested, taking into account adhesion force acting in the direction normal to the contact surface. At each scale level, the contact problem for a 3D periodic wavy indenter is solved by using the strip method to reduce the problem to 2D formulation in a strip. Different regimes of contact and adhesion interaction are possible in each strip, including partial and saturated contact. The friction force is calculated as a sum of two terms. The first term is due to hysteretic losses occurring when asperities of this scale level cyclically deform the viscoelastic foundation during sliding. The second term is the law of friction determined from the solution of the contact problem at the inferior scale level. For the case of a two-level wavy surface, the contribution of both levels into the total friction force is calculated and analyzed depending on the sliding velocity and specific energy of adhesion of the contacting surfaces.

scholarly journals Mathematics and Poetry • Unification, Unity, Union

Sci ◽  
2020 ◽  
Vol 2 (3) ◽  
pp. 58
Author(s):  
Florin F. Nichita
Keyword(s):  
Differential Geometry ◽  
Baxter Equation ◽  
Dual Numbers ◽  
Euler’S Formula ◽  
Euler’S Identity

We consider a multitude of topics in mathematics where unification constructions play an important role: the Yang–Baxter equation and its modified version, Euler’s formula for dual numbers, means and their inequalities, topics in differential geometry, etc. It is interesting to observe that the idea of unification (unity and union) is also present in poetry. Moreover, Euler’s identity is a source of inspiration for the post-modern poets.

Influence of the Lead Angle from the Vertical Axis Milling on Effective Radius of the Cutter

2013 ◽  
Vol 581 ◽  
pp. 44-49 ◽  
Author(s):  
Jozef Peterka ◽  
Peter Pokorný
Keyword(s):  
Contact Line ◽  
Contact Surface ◽  
Vertical Axis ◽  
Effective Radius ◽  
Technological Parameters ◽  
Machined Surface ◽  
Lead Angle ◽  
Finishing Process ◽  
Five Axis

The submission deals with the five-axis milling at finishing process by the nose ball milling cutter. The final quality of machined surfaces is depending on many technological parameters. One of these parameters is the effective radius of cutter too. The effective radius of cutter determinates the contact line if you like the contact surface between cutter and just machined surface. In the submission is described the effect of a lead angle from the vertical axis milling on the effective radius of cutter. At last it is remitted how the change of effective radius is reflected in practice.

scholarly journals The Multiobjective Optimization of a Prismatic Drive

2007 ◽  
Author(s):  
E´milie Bouyer ◽  
Ste´phane Caro ◽  
Damien Chablat ◽  
Jorge Angeles
Keyword(s):  
Multiobjective Optimization ◽  
Contact Surface ◽  
Performance Index ◽  
Pareto Frontier ◽  
Rolling Motion ◽  
Objective Functions ◽  
Cam Mechanism ◽  
Pressure Angle ◽  
Pure Rolling

The multiobjective optimization of Slide-o-Cam is reported in this paper. Slide-o-Cam is a cam mechanism with multiple rollers mounted on a common translating follower. This transmission provides pure-rolling motion, thereby reducing the friction of rack-and-pinions and linear drives. A Pareto frontier is obtained by means of multiobjective optimization. This optimization is based on three objective functions: (i) the pressure angle, which is a suitable performance index for the transmission because it determines the amount of force transmitted to the load vs. that transmitted to the machine frame; (ii) the Hertz pressure used to evaluate the stresses produced on the contact surface between cam and roller; and (iii) the size of the mechanism, characterized by the number of cams and their width.

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