Upload
khmer-cham
View
221
Download
0
Embed Size (px)
Citation preview
7/23/2019 Presentation Tecca
1/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
On the Use of GeoGebra for Path Curvature Analysisin Linkage Design
23 January 2014
University of Rome Tor Vergata
Federico Tecca
http://find/7/23/2019 Presentation Tecca
2/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Summary:
Introduction,
Kinematic Synthesis for Infinitesimally Separated
Positions:Mechanism simulation,Three Infinitesimally Separated Link Positions,Four Infinitesimally Separated Link Positions,
How to use the .ggb files,
GeoGebra STEM 2013,
Conclusions.
http://find/7/23/2019 Presentation Tecca
3/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Introduction
http://find/7/23/2019 Presentation Tecca
4/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Aim of the work:
Is to summarise graphical methods of MechanicalEngineering formulated in the past and subsequentlyabandoned because of their complexity in representation
and construction when available tools were not suitable.
http://find/http://goback/7/23/2019 Presentation Tecca
5/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Aim of the work:
Is to summarise graphical methods of MechanicalEngineering formulated in the past and subsequentlyabandoned because of their complexity in representation
and construction when available tools were not suitable.
http://find/7/23/2019 Presentation Tecca
6/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
In particular for Kinematic Synthesis for Infinitesimally
Separated Positions:
We want to draw the notable locii for the Kinematic
Synthesis for Infinitesimally Separated Positions.
http://find/7/23/2019 Presentation Tecca
7/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
In particular for Kinematic Synthesis for Infinitesimally
Separated Positions:
We want to draw the notable locii for the Kinematic
Synthesis for Infinitesimally Separated Positions.
Question:
We want to develop parametric worksheets. In these itspossible to change the input parameters and then theworksheet designs the mechanism and the notable lociifor another configuration.
http://find/7/23/2019 Presentation Tecca
8/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
The features of the sofware must be:
http://find/7/23/2019 Presentation Tecca
9/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
The features of the sofware must be:
Flexibility,
http://find/7/23/2019 Presentation Tecca
10/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
The features of the sofware must be:
Flexibility,
Intuitivness,
http://find/http://goback/7/23/2019 Presentation Tecca
11/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
The features of the sofware must be:
Flexibility,
Intuitivness,
Parametricity.
http://find/7/23/2019 Presentation Tecca
12/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
The features of the sofware must be:
Flexibility,
Intuitivness,
Parametricity.
Choice
http://find/7/23/2019 Presentation Tecca
13/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
The features of the sofware must be:
Flexibility,
Intuitivness,
Parametricity.
Choice Software GeoGebra , is the answer to theproblem.
http://find/http://goback/7/23/2019 Presentation Tecca
14/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
GeoGebra STEM 2013 GeoGebra InternationalInstitute
http://find/7/23/2019 Presentation Tecca
15/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
GeoGebra STEM 2013 GeoGebra InternationalInstitute
Supervised by CCITE(Cambridge Center forInnovation in Technological Education)
.
http://find/http://goback/7/23/2019 Presentation Tecca
16/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
A new section of the web sitehttp://www.geogebraitalia.org/ was createdfor these materials.
this is dedicated to the engineering applications onGeoGebra,http://engineering.geogebraitalia.org/
http://www.geogebraitalia.org/http://engineering.geogebraitalia.org/http://engineering.geogebraitalia.org/http://www.geogebraitalia.org/http://find/http://goback/7/23/2019 Presentation Tecca
17/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
A new section of the web sitehttp://www.geogebraitalia.org/ was createdfor these materials.
this is dedicated to the engineering applications onGeoGebra,http://engineering.geogebraitalia.org/
Part of the work was discussed for the bachelor thesisParametric Kinematic Synthesis of Linkages for
Prescribed Infinitesimally Separated Positions.
http://www.geogebraitalia.org/http://engineering.geogebraitalia.org/http://engineering.geogebraitalia.org/http://www.geogebraitalia.org/http://find/7/23/2019 Presentation Tecca
18/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Kinematic Synthesis for InfinitesimallySeparated Positions
http://find/http://goback/7/23/2019 Presentation Tecca
19/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Mechanisms simulation
http://find/7/23/2019 Presentation Tecca
20/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Mechanisms simulation
= 0.6
d= 0.5
l= 1.7
s= 0.9
A0
= 0.93
http://find/7/23/2019 Presentation Tecca
21/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Mechanisms simulation
= 0.6
d= 0.5
l= 1.7
s= 0.9
A0
= 0.93
A
A : (s cos, s sin)
http://find/7/23/2019 Presentation Tecca
22/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Mechanisms simulation
= 0.6
d= 0.5
l= 1.7
s= 0.9
A0
= 0.93
A
A : (s cos, s sin)
r = l
saxis = x tan
d
http://find/http://goback/7/23/2019 Presentation Tecca
23/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Mechanisms simulation
= 0.6
d= 0.5
l= 1.7
s= 0.9
A0
= 0.93
A
A : (s cos, s sin)
r = l
saxis = x tan
dB
http://find/7/23/2019 Presentation Tecca
24/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Mechanisms simulation
= 0.6
d= 0.5
l= 1.7
s= 0.9
A0
= 0.93
A
A : (s cos, s sin)
r = l
saxis = x tan
dB
http://find/7/23/2019 Presentation Tecca
25/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Three Infinitesimally Separated LinkPositions
http://find/7/23/2019 Presentation Tecca
26/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Inflection Circle
http://find/http://goback/7/23/2019 Presentation Tecca
27/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
The second expression of the Euler-Savary formula is usedto design the Inflection CircleF :
P0M2 = M MM, (1)
Point M, on the Inflection CircleF:
MM=P0M
2
M , (2)
http://find/7/23/2019 Presentation Tecca
28/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
The second expression of the Euler-Savary formula is usedto design the Inflection CircleF :
P0M2 = M MM, (1)
Point M, on the Inflection CircleF:
MM=P0M
2
M , (2)
The distances P0M e Mof the known points arecalculated and then the Inflection CirlceF is designed,computing MM from (2).
http://find/7/23/2019 Presentation Tecca
29/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Inflection Circle
A0
L1 = 5.2= 0.5
A
L2 = 5.5
B0
Lgl= 11.5
BL3 = 3.3L4 = 3 C
P15
http://find/7/23/2019 Presentation Tecca
30/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Inflection Circle
A0
L1 = 5.2= 0.5
A
L2 = 5.5
B0
Lgl= 11.5
BL3 = 3.3L4 = 3 C
P15
http://find/7/23/2019 Presentation Tecca
31/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Inflection Circle
A0
L1 = 5.2= 0.5
A
L2 = 5.5
B0
Lgl= 11.5
BL3 = 3.3L4 = 3 C
P15
r = P15 B
2
B0 B
http://find/http://goback/7/23/2019 Presentation Tecca
32/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Inflection Circle
A0
L1 = 5.2= 0.5
A
L2 = 5.5
B0
Lgl= 11.5
BL3 = 3.3L4 = 3 C
P15
r = P15 B
2
B0 B
B1
http://find/http://goback/7/23/2019 Presentation Tecca
33/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Inflection Circle
A0
L1 = 5.2= 0.5
A
L2 = 5.5
B0
Lgl= 11.5
BL3 = 3.3L4 = 3 C
P15
r = P15 B
2
B0 B
B1
http://find/http://goback/7/23/2019 Presentation Tecca
34/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Four Infinitesimally Separated LinkPositions
http://find/http://goback/7/23/2019 Presentation Tecca
35/69
7/23/2019 Presentation Tecca
36/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Cubic of Stationary Curvature
The design of the Cubic of Stationary CurvatureK ismade with geometric construction too. In particular theCartesian form of the Cubic of Stationary CurvatureK:
x2 +y2
Ny +
x2 +y2
Mx = 1 , (3)
this is separated in a system of two equations:
x
2
+y2 x= 0
x2 +y2 y= 0 (4)
With this method the intersection between the twoequations, two circles, correspond to a point on the Cubic
of Stationary CurvatureK.
http://find/http://goback/7/23/2019 Presentation Tecca
37/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
N ed Mare the geometric invariants of the Cubic ofStationary Curvature. These are determined from twopoints,A e B, on the Cubic of Stationary Curvature.
From these points its possible to reach the equations:N= hAhBsin(BA)(cosAcosB(hAsinBhBsinA))M=N hAcosA((NcosAhA)sinA)
, (5)
Where A, Bare the angles between the segments P0Ae P0Bwith the normal vector
N, vector of the Canonical
reference, and hA, hB the distances from A and B to P0.
http://find/7/23/2019 Presentation Tecca
38/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Cubic of Stationary Curvature
N
T
P0
http://find/7/23/2019 Presentation Tecca
39/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Cubic of Stationary Curvature
N
T
P0
S(M, 0)
R(0,N)
http://find/7/23/2019 Presentation Tecca
40/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Cubic of Stationary Curvature
N
T
P0
S(M, 0)
R(0,N)
A(, )
http://find/7/23/2019 Presentation Tecca
41/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Cubic of Stationary Curvature
N
T
P0
S(M, 0)
R(0,N)
A(, )
http://find/http://goback/7/23/2019 Presentation Tecca
42/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Cubic of Stationary Curvature
N
T
P0
S(M, 0)
R(0,N)
A(, )(0, )
(, 0)
http://find/http://goback/7/23/2019 Presentation Tecca
43/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Cubic of Stationary Curvature
N
T
P0
S(M, 0)
R(0,N)
A(, )(0, )
(, 0)
K
http://find/http://goback/7/23/2019 Presentation Tecca
44/69
On the Use ofGeoGebra for Path
Curvature Analysis inLinkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Cubic of Stationary Curvature
N
T
P0
S(M, 0)
R(0,N)
A(, )(0, )
(, 0)
K
http://find/http://goback/7/23/2019 Presentation Tecca
45/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Cubic of Stationary Curvature
N
T
a
A(, )
S(M, 0)
R(0,N)
K
P0
(0, )
(, 0)
http://find/http://goback/7/23/2019 Presentation Tecca
46/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Cubic of Stationary Curvature
N
T
a
A(, )
S(M, 0)
R(0,N)
K
P0
(0, )
(, 0)
http://find/7/23/2019 Presentation Tecca
47/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Example applied to a mechanism
C
= 0.87rad
L1 = 4.5B02 = 1.3
= 2rad
AL3 = 7
BLgl= 7.8
P14
http://find/7/23/2019 Presentation Tecca
48/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Pivot Point Curvature
http://find/http://goback/7/23/2019 Presentation Tecca
49/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Example applied to a mechanism
A0
L1 = 1.5 = 1.26
A
L2 = 1.44
L3 = 2.12L4 = 2
B0
B
P13
http://find/7/23/2019 Presentation Tecca
50/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Its possible to compute the centre of curvature of thepoints on the Cubic of Stationary Curvature
Kwith a
geometric construction on GeoGebra using the secondexpression of the Euler-Savary formula:
Pivot Point Curvature
http://find/7/23/2019 Presentation Tecca
51/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
How to use the .ggb files
http://find/http://goback/7/23/2019 Presentation Tecca
52/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Notable locii varying the anomaly angle .
http://find/7/23/2019 Presentation Tecca
53/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Notable locii varying the input parameters.
http://find/http://goback/7/23/2019 Presentation Tecca
54/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
GeoGebra STEM 2013
http://find/7/23/2019 Presentation Tecca
55/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
For the competition organized by the GeoGebraInternational Institute, GeoGebra STEM 2013, othermaterials were made.
In particular the materials are developed in:Fluid Dynamics,
Strength of Materials.
All the worksheets are collected in the web sitehttp://engineering.geogebraitalia.org/.
http://engineering.geogebraitalia.org/http://engineering.geogebraitalia.org/http://find/7/23/2019 Presentation Tecca
56/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Boundary Layer
http://find/7/23/2019 Presentation Tecca
57/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
In a thin Boundary Layer near the solid boundary, shearforces must necessarily be significant because of the largeshearing deformations resulting from the fluids being atrest at the solid boundary.
This fact generates high gradients at the interfaceflatbed-fluid and the creation of the Boundary Layer.
http://find/http://goback/7/23/2019 Presentation Tecca
58/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Its possible to demonstrate that the function thatdescribed the Boundary Layer, with some approximation:
=LU
= L
Re, (6)
http://find/http://goback/7/23/2019 Presentation Tecca
59/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Its possible to demonstrate that the function thatdescribed the Boundary Layer, with some approximation:
=LU
= L
Re, (6)
where:
L is the length of the flatbed,
Reis the Reynolds number,
U is the speed of the fluid,is the cinematic viscosity of the fluid.
http://find/http://goback/7/23/2019 Presentation Tecca
60/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
http://find/7/23/2019 Presentation Tecca
61/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Force in a Nozzle
http://find/7/23/2019 Presentation Tecca
62/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
The starting point is the conservation of the momentum:
F=dQ
dt , (7)
http://find/7/23/2019 Presentation Tecca
63/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
The starting point is the conservation of the momentum:
F=dQ
dt , (7)
Through the Reynolds theorem and some othersimplification its possible to obtain the application formof the conservation of the momentum:
F=
Ni=1 (
uun
+pn
)iSi (8)
http://find/7/23/2019 Presentation Tecca
64/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
u2 = 6.2
2 = 3.32rad
E
r2 = 1.2
A
1 = 0.7rad
r1 = 1.4
u1 = 3.8
Force
http://find/7/23/2019 Presentation Tecca
65/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Force in a Nozzle.
http://find/7/23/2019 Presentation Tecca
66/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Conclusions
http://find/7/23/2019 Presentation Tecca
67/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
A library with some of the materials created is made.These GeoGebra worksheets are totally parametric and
they resolve some problems for Mechanical Engineering.
http://find/7/23/2019 Presentation Tecca
68/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
A library with some of the materials created is made.These GeoGebra worksheets are totally parametric and
they resolve some problems for Mechanical Engineering.
The solutions to these problems are graphic andgeometric constructions.
http://find/7/23/2019 Presentation Tecca
69/69
On the Use ofGeoGebra for Path
Curvature Analysis in
Linkage Design
Federico Tecca
Introduction
Aim of the work
Choosen Software
Work partecipation
Kinematic Synthesis forInfinitesimallySeparated Positions
Mechanisms simulation
Three InfinitesimallySeparated Link Positions
Inflection Circle
Four InfinitesimallySeparated Link Positions
How to use the .ggbfiles
GeoGebra STEM 2013
Boundary Layer
Force in a Nozzle
Conclusions
Thank you for the attention
http://find/http://goback/