recreating old mechanisme
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recreating old mechanisme
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I'm recreating an old mechanisme in 3d modeling software. The idea is that this triangular shape rotates around an off-center axis. This will create 4 phases. first (like in the picture) the construction L is down and stay stable in that position (which means the parts of the triangle thing that touch the construct L are partially circle. In the next phase the construction moves up, then it is stable again and in the last phase it moves down.
Questions are: what is the mathematics involved in the shape assuming it never looses contact with the construct L. Initially I made the sides out of 6 circular elements (arcs), but I'm not sure if that is even the correct shape. Once I have the shape, what is the position of L as function of the rotation of the object?
mechanisms
asked 8 hours ago
fransfrans
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I'm recreating an old mechanisme in 3d modeling software. The idea is that this triangular shape rotates around an off-center axis. This will create 4 phases. first (like in the picture) the construction L is down and stay stable in that position (which means the parts of the triangle thing that touch the construct L are partially circle. In the next phase the construction moves up, then it is stable again and in the last phase it moves down.
Questions are: what is the mathematics involved in the shape assuming it never looses contact with the construct L. Initially I made the sides out of 6 circular elements (arcs), but I'm not sure if that is even the correct shape. Once I have the shape, what is the position of L as function of the rotation of the object?
mechanisms
asked 8 hours ago
fransfrans
111 bronze badge
New contributor
frans is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment
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$begingroup$
I'm recreating an old mechanisme in 3d modeling software. The idea is that this triangular shape rotates around an off-center axis. This will create 4 phases. first (like in the picture) the construction L is down and stay stable in that position (which means the parts of the triangle thing that touch the construct L are partially circle. In the next phase the construction moves up, then it is stable again and in the last phase it moves down.
Questions are: what is the mathematics involved in the shape assuming it never looses contact with the construct L. Initially I made the sides out of 6 circular elements (arcs), but I'm not sure if that is even the correct shape. Once I have the shape, what is the position of L as function of the rotation of the object?
mechanisms
asked 8 hours ago
fransfrans
111 bronze badge
New contributor
frans is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I'm recreating an old mechanisme in 3d modeling software. The idea is that this triangular shape rotates around an off-center axis. This will create 4 phases. first (like in the picture) the construction L is down and stay stable in that position (which means the parts of the triangle thing that touch the construct L are partially circle. In the next phase the construction moves up, then it is stable again and in the last phase it moves down.
Questions are: what is the mathematics involved in the shape assuming it never looses contact with the construct L. Initially I made the sides out of 6 circular elements (arcs), but I'm not sure if that is even the correct shape. Once I have the shape, what is the position of L as function of the rotation of the object?
mechanisms
mechanisms
asked 8 hours ago
fransfrans
111 bronze badge
New contributor
frans is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
fransfrans
111 bronze badge
New contributor
frans is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
fransfrans
111 bronze badge
New contributor
frans is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
fransfrans
111 bronze badge
asked 8 hours ago
fransfrans
111 bronze badge
111 bronze badge
New contributor
frans is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Check out our Code of Conduct.
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3 Answers
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$begingroup$
I think you are looking for a "curve of constant width".
Figure 1. Construction diagram for generating a curve of constant width from a triangle. Source: Curve of constant width.
Curves of constant width can be generated by joining circular arcs centered on the vertices of a regular or irregular convex polygon with an odd number of sides (triangle, pentagon, heptagon, etc.).
answered 8 hours ago
TransistorTransistor
1,0944 silver badges12 bronze badges
$endgroup$
2
$begingroup$
When you design cam mechanisms it would be s good idea to ensure that the curve is continious to the third derivate of position (derivates being velocity, acceleration, jerk ( followed by snap, crackle and pop))
$endgroup$
– joojaa
7 hours ago
add a comment
|
$begingroup$
great reference to curves-of-constant-width. It shows that my initial setup build out of circular great reference to curves-of-constant-width. Thank you! It shows that my initial setup build out of circular arcs is correct. In my case I decide a=b=c in the picture you used above.
So the question still is, what would be the function that describes the movement of L when it goes from the lower to the upper position (or the reverse) as function of the rotation.
answered 5 hours ago
illuillu
12 bronze badges
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illu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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1
$begingroup$
This is not an answer to the question so it has been flagged for deletion. Please take the Tour to learn how the site works and then you can ask your own question.
$endgroup$
– Transistor
5 hours ago
$begingroup$
problem is I cannot add comments to it because I need 50 reputation points first. That's why I had to create an 'answer'. Sorry Transistor.
$endgroup$
– illu
2 hours ago
$begingroup$
@StainlessSteelRat I already managed to create the shape, by using 3 big circles and 3 small circles and put them in the right place so they touch smoothly. More or less like in the picture by transistor. I don't understand the green lines in your pictures. What I'm looking for is a kind of formula that tells me the vertical position of part L as a function of the rotation angle of the triangular part C
$endgroup$
– illu
2 hours ago
add a comment
|
$begingroup$
To create your triangular pick shape, you need two equilateral triangles, centered on each other. Your spline should make contact with each of the corners of the triangles.
The ratio of lengths between the two triangles will give you the curvature.
Your ultimate problem is you don't have dimensions so you can do your math. This SolidWorks drawing will give you the dimensions to build your slot.
Two rotations of Part C will give you the dimensions of your guideway.
answered 4 hours ago
StainlessSteelRatStainlessSteelRat
4794 silver badges7 bronze badges
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I think you are looking for a "curve of constant width".
Figure 1. Construction diagram for generating a curve of constant width from a triangle. Source: Curve of constant width.
Curves of constant width can be generated by joining circular arcs centered on the vertices of a regular or irregular convex polygon with an odd number of sides (triangle, pentagon, heptagon, etc.).
answered 8 hours ago
TransistorTransistor
1,0944 silver badges12 bronze badges
$endgroup$
2
$begingroup$
When you design cam mechanisms it would be s good idea to ensure that the curve is continious to the third derivate of position (derivates being velocity, acceleration, jerk ( followed by snap, crackle and pop))
$endgroup$
– joojaa
7 hours ago
add a comment
|
$begingroup$
I think you are looking for a "curve of constant width".
Figure 1. Construction diagram for generating a curve of constant width from a triangle. Source: Curve of constant width.
Curves of constant width can be generated by joining circular arcs centered on the vertices of a regular or irregular convex polygon with an odd number of sides (triangle, pentagon, heptagon, etc.).
answered 8 hours ago
TransistorTransistor
1,0944 silver badges12 bronze badges
$endgroup$
2
$begingroup$
When you design cam mechanisms it would be s good idea to ensure that the curve is continious to the third derivate of position (derivates being velocity, acceleration, jerk ( followed by snap, crackle and pop))
$endgroup$
– joojaa
7 hours ago
add a comment
|
$begingroup$
I think you are looking for a "curve of constant width".
Figure 1. Construction diagram for generating a curve of constant width from a triangle. Source: Curve of constant width.
Curves of constant width can be generated by joining circular arcs centered on the vertices of a regular or irregular convex polygon with an odd number of sides (triangle, pentagon, heptagon, etc.).
answered 8 hours ago
TransistorTransistor
1,0944 silver badges12 bronze badges
$endgroup$
I think you are looking for a "curve of constant width".
Figure 1. Construction diagram for generating a curve of constant width from a triangle. Source: Curve of constant width.
Curves of constant width can be generated by joining circular arcs centered on the vertices of a regular or irregular convex polygon with an odd number of sides (triangle, pentagon, heptagon, etc.).
answered 8 hours ago
TransistorTransistor
1,0944 silver badges12 bronze badges
answered 8 hours ago
TransistorTransistor
1,0944 silver badges12 bronze badges
answered 8 hours ago
TransistorTransistor
1,0944 silver badges12 bronze badges
answered 8 hours ago
TransistorTransistor
1,0944 silver badges12 bronze badges
1,0944 silver badges12 bronze badges
2
$begingroup$
When you design cam mechanisms it would be s good idea to ensure that the curve is continious to the third derivate of position (derivates being velocity, acceleration, jerk ( followed by snap, crackle and pop))
$endgroup$
– joojaa
7 hours ago
add a comment
|
2
$begingroup$
When you design cam mechanisms it would be s good idea to ensure that the curve is continious to the third derivate of position (derivates being velocity, acceleration, jerk ( followed by snap, crackle and pop))
$endgroup$
– joojaa
7 hours ago
2
2
$begingroup$
When you design cam mechanisms it would be s good idea to ensure that the curve is continious to the third derivate of position (derivates being velocity, acceleration, jerk ( followed by snap, crackle and pop))
$endgroup$
– joojaa
7 hours ago
$begingroup$
When you design cam mechanisms it would be s good idea to ensure that the curve is continious to the third derivate of position (derivates being velocity, acceleration, jerk ( followed by snap, crackle and pop))
$endgroup$
– joojaa
7 hours ago
add a comment
|
$begingroup$
great reference to curves-of-constant-width. It shows that my initial setup build out of circular great reference to curves-of-constant-width. Thank you! It shows that my initial setup build out of circular arcs is correct. In my case I decide a=b=c in the picture you used above.
So the question still is, what would be the function that describes the movement of L when it goes from the lower to the upper position (or the reverse) as function of the rotation.
answered 5 hours ago
illuillu
12 bronze badges
New contributor
illu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
This is not an answer to the question so it has been flagged for deletion. Please take the Tour to learn how the site works and then you can ask your own question.
$endgroup$
– Transistor
5 hours ago
$begingroup$
problem is I cannot add comments to it because I need 50 reputation points first. That's why I had to create an 'answer'. Sorry Transistor.
$endgroup$
– illu
2 hours ago
$begingroup$
@StainlessSteelRat I already managed to create the shape, by using 3 big circles and 3 small circles and put them in the right place so they touch smoothly. More or less like in the picture by transistor. I don't understand the green lines in your pictures. What I'm looking for is a kind of formula that tells me the vertical position of part L as a function of the rotation angle of the triangular part C
$endgroup$
– illu
2 hours ago
add a comment
|
$begingroup$
great reference to curves-of-constant-width. It shows that my initial setup build out of circular great reference to curves-of-constant-width. Thank you! It shows that my initial setup build out of circular arcs is correct. In my case I decide a=b=c in the picture you used above.
So the question still is, what would be the function that describes the movement of L when it goes from the lower to the upper position (or the reverse) as function of the rotation.
answered 5 hours ago
illuillu
12 bronze badges
New contributor
illu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
This is not an answer to the question so it has been flagged for deletion. Please take the Tour to learn how the site works and then you can ask your own question.
$endgroup$
– Transistor
5 hours ago
$begingroup$
problem is I cannot add comments to it because I need 50 reputation points first. That's why I had to create an 'answer'. Sorry Transistor.
$endgroup$
– illu
2 hours ago
$begingroup$
@StainlessSteelRat I already managed to create the shape, by using 3 big circles and 3 small circles and put them in the right place so they touch smoothly. More or less like in the picture by transistor. I don't understand the green lines in your pictures. What I'm looking for is a kind of formula that tells me the vertical position of part L as a function of the rotation angle of the triangular part C
$endgroup$
– illu
2 hours ago
add a comment
|
$begingroup$
great reference to curves-of-constant-width. It shows that my initial setup build out of circular great reference to curves-of-constant-width. Thank you! It shows that my initial setup build out of circular arcs is correct. In my case I decide a=b=c in the picture you used above.
So the question still is, what would be the function that describes the movement of L when it goes from the lower to the upper position (or the reverse) as function of the rotation.
answered 5 hours ago
illuillu
12 bronze badges
New contributor
illu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
great reference to curves-of-constant-width. It shows that my initial setup build out of circular great reference to curves-of-constant-width. Thank you! It shows that my initial setup build out of circular arcs is correct. In my case I decide a=b=c in the picture you used above.
So the question still is, what would be the function that describes the movement of L when it goes from the lower to the upper position (or the reverse) as function of the rotation.
answered 5 hours ago
illuillu
12 bronze badges
New contributor
illu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 5 hours ago
illuillu
12 bronze badges
New contributor
illu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 5 hours ago
illuillu
12 bronze badges
answered 5 hours ago
illuillu
12 bronze badges
12 bronze badges
New contributor
illu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
illu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
This is not an answer to the question so it has been flagged for deletion. Please take the Tour to learn how the site works and then you can ask your own question.
$endgroup$
– Transistor
5 hours ago
$begingroup$
problem is I cannot add comments to it because I need 50 reputation points first. That's why I had to create an 'answer'. Sorry Transistor.
$endgroup$
– illu
2 hours ago
$begingroup$
@StainlessSteelRat I already managed to create the shape, by using 3 big circles and 3 small circles and put them in the right place so they touch smoothly. More or less like in the picture by transistor. I don't understand the green lines in your pictures. What I'm looking for is a kind of formula that tells me the vertical position of part L as a function of the rotation angle of the triangular part C
$endgroup$
– illu
2 hours ago
add a comment
|
1
$begingroup$
This is not an answer to the question so it has been flagged for deletion. Please take the Tour to learn how the site works and then you can ask your own question.
$endgroup$
– Transistor
5 hours ago
$begingroup$
problem is I cannot add comments to it because I need 50 reputation points first. That's why I had to create an 'answer'. Sorry Transistor.
$endgroup$
– illu
2 hours ago
$begingroup$
@StainlessSteelRat I already managed to create the shape, by using 3 big circles and 3 small circles and put them in the right place so they touch smoothly. More or less like in the picture by transistor. I don't understand the green lines in your pictures. What I'm looking for is a kind of formula that tells me the vertical position of part L as a function of the rotation angle of the triangular part C
$endgroup$
– illu
2 hours ago
1
1
$begingroup$
This is not an answer to the question so it has been flagged for deletion. Please take the Tour to learn how the site works and then you can ask your own question.
$endgroup$
– Transistor
5 hours ago
$begingroup$
This is not an answer to the question so it has been flagged for deletion. Please take the Tour to learn how the site works and then you can ask your own question.
$endgroup$
– Transistor
5 hours ago
$begingroup$
problem is I cannot add comments to it because I need 50 reputation points first. That's why I had to create an 'answer'. Sorry Transistor.
$endgroup$
– illu
2 hours ago
$begingroup$
problem is I cannot add comments to it because I need 50 reputation points first. That's why I had to create an 'answer'. Sorry Transistor.
$endgroup$
– illu
2 hours ago
$begingroup$
@StainlessSteelRat I already managed to create the shape, by using 3 big circles and 3 small circles and put them in the right place so they touch smoothly. More or less like in the picture by transistor. I don't understand the green lines in your pictures. What I'm looking for is a kind of formula that tells me the vertical position of part L as a function of the rotation angle of the triangular part C
$endgroup$
– illu
2 hours ago
$begingroup$
@StainlessSteelRat I already managed to create the shape, by using 3 big circles and 3 small circles and put them in the right place so they touch smoothly. More or less like in the picture by transistor. I don't understand the green lines in your pictures. What I'm looking for is a kind of formula that tells me the vertical position of part L as a function of the rotation angle of the triangular part C
$endgroup$
– illu
2 hours ago
add a comment
|
$begingroup$
To create your triangular pick shape, you need two equilateral triangles, centered on each other. Your spline should make contact with each of the corners of the triangles.
The ratio of lengths between the two triangles will give you the curvature.
Your ultimate problem is you don't have dimensions so you can do your math. This SolidWorks drawing will give you the dimensions to build your slot.
Two rotations of Part C will give you the dimensions of your guideway.
answered 4 hours ago
StainlessSteelRatStainlessSteelRat
4794 silver badges7 bronze badges
$endgroup$
add a comment
|
$begingroup$
To create your triangular pick shape, you need two equilateral triangles, centered on each other. Your spline should make contact with each of the corners of the triangles.
The ratio of lengths between the two triangles will give you the curvature.
Your ultimate problem is you don't have dimensions so you can do your math. This SolidWorks drawing will give you the dimensions to build your slot.
Two rotations of Part C will give you the dimensions of your guideway.
answered 4 hours ago
StainlessSteelRatStainlessSteelRat
4794 silver badges7 bronze badges
$endgroup$
add a comment
|
$begingroup$
To create your triangular pick shape, you need two equilateral triangles, centered on each other. Your spline should make contact with each of the corners of the triangles.
The ratio of lengths between the two triangles will give you the curvature.
Your ultimate problem is you don't have dimensions so you can do your math. This SolidWorks drawing will give you the dimensions to build your slot.
Two rotations of Part C will give you the dimensions of your guideway.
answered 4 hours ago
StainlessSteelRatStainlessSteelRat
4794 silver badges7 bronze badges
$endgroup$
To create your triangular pick shape, you need two equilateral triangles, centered on each other. Your spline should make contact with each of the corners of the triangles.
The ratio of lengths between the two triangles will give you the curvature.
Your ultimate problem is you don't have dimensions so you can do your math. This SolidWorks drawing will give you the dimensions to build your slot.
Two rotations of Part C will give you the dimensions of your guideway.
answered 4 hours ago
StainlessSteelRatStainlessSteelRat
4794 silver badges7 bronze badges
edited 3 hours ago
answered 4 hours ago
StainlessSteelRatStainlessSteelRat
4794 silver badges7 bronze badges
answered 4 hours ago
StainlessSteelRatStainlessSteelRat
4794 silver badges7 bronze badges
answered 4 hours ago
StainlessSteelRatStainlessSteelRat
4794 silver badges7 bronze badges
4794 silver badges7 bronze badges
add a comment
|
add a comment
|
frans is a new contributor. Be nice, and check out our Code of Conduct.
frans is a new contributor. Be nice, and check out our Code of Conduct.
frans is a new contributor. Be nice, and check out our Code of Conduct.
frans is a new contributor. Be nice, and check out our Code of Conduct.
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