How to draw Cam lobe

[Lee Mac]

Constrained by the given dimensions, I don't believe all four arcs can be cotangent.

 

After constructing the first three arcs to be cotangent and adhering to the given arc dimensions, the radii for a cotangent fourth arc (shown below in yellow) are unequal:

 

 

Unless I am mistaken, for all four arcs to be cotangent, some dimensions must change.

[JD Mather]

Constrained by the given dimensions, I don't believe all four arcs can be cotangent.

 

Unless I am mistaken, for all four arcs to be cotangent, some dimensions must change.

 

No dimensions need to be changed - you haven't looked at my solution. The center of R45 is not on any line - it is not concentric with the hole.

[JD Mather]

It's work! I finally got it ...

Are you sure about that? Attach your "solution" here.

[JD Mather]

.... my post was predominantly aimed at showing how I would go about constructing the cam in AutoCAD (via geometric construction) using the dimensional information provided.

 

There is no dimensional information provided that indicates the R45 is concentric with the hole for the shaft.

Tangency is not possible all around the cam with a solution that makes that assumption (given that it is an assumption for the R45 to be concentric).

 

On the other hand if the assumption is that all arcs are tangent then there is a unique solution that requires only the dimensions given - no more and no less.

[Lee Mac]

There is no dimensional information provided that indicates the R45 is concentric with the hole for the shaft.

 

Good point - this was an incorrect assumption in my construction.

[Lee Mac]

There is no dimensional information provided that indicates the R45 is concentric with the hole for the shaft.

 

JD, Looking back at the diagram, surely the R45 arc spanning 90 degrees implies concentricity with the shaft?

[JD Mather]

Which makes more logical sense - all arcs tangent and endpoint coincident or R45 concentric? Have to choose one or the other (in this case).

How can an assumption be made that any arcs are tangent if they are not all tangent?

I thought it was interesting to discover that there is one unique solution with only the information given if all arcs are assumed to be tangent and no other assumptions.

[Lee Mac]

Which makes more logical sense - all arcs tangent and endpoint coincident or R45 concentric? Have to choose one or the other (in this case).

 

If R45 is not concentric, the angular measurements are surely meaningless since they do not pass through the arc endpoints - what exactly are they dimensioning?

 

If the angular dimensions need not pass through the arc end points, the shaft could be placed anywhere within the cam.

[JD Mather]

If R45 is not concentric, the angular measurements are surely meaningless since they do not pass through the arc endpoints - ....

 

But they do pass through the arc endpoints.

 

Here is Creo (Pro/E) solution (of course, same as the other solutions I've posted).

You can see the blue dots indicating the arc endpoints of the arcs on the lines.

Notice also the T for tangents between arcs.

 

 

Post #32 shows AutoCAD solution with Coincident endpoints and Tangent curves.

Post # 47 shows the same for SolidWorks.

[Lee Mac]

But they do pass through the arc endpoints.

 

My apologies JD, I was hung up on the R45 arc spanning 90 degrees - a false assumption.

Thank you for your correction!

[Bill Tillman]

This has been an interesting excercise to attempt and to follow the progress others made with it. Like some of the other replies, I made assumptions which did not fly even though ended up with a fully constrained shape. Makes one wonder what will really happen when this thing is mounted on a shaft and starts moving some lever or pushrod device. And what RPM's will it work at?

[neophoible]

If R45 is not concentric, the angular measurements are surely meaningless since they do not pass through the arc endpoints - what exactly are they dimensioning?

 

If the angular dimensions need not pass through the arc end points, the shaft could be placed anywhere within the cam.

I'm not sure the original intent of the problem was so complicated, but JD's solutions must be correct given the expectations of a cam to have cotangency all along its surface.

 

I explained earlier that the angular dimensions refer to the rotation of the cam about the center point of the shaft, which makes sense for a cam or any rotating part. If you had completed your original construction with cotangency for the final arc, I think your solution would have been the same as Bill's and as my original misinterpretation. Bill posted his. I did not bother to post mine when I realized that the final endpoints would not match up.

[neophoible]

This has been an interesting excercise to attempt and to follow the progress others made with it. Like some of the other replies, I made assumptions which did not fly even though ended up with a fully constrained shape. Makes one wonder what will really happen when this thing is mounted on a shaft and starts moving some lever or pushrod device. And what RPM's will it work at?

I'm not so sure that the initial assumptions were out of order. As I said in response to one of Lee's comments, this problem may not have been intended to be quite as difficult to lay out as it actually is, especially without invoking geometric and dimensional constraints. I suspect conversions & tolerances may have affected it somewhat. I'd be interested in seeing JD's solution superimposed on the drawing in the OP. I strongly suspect that the 45R is essentially concentric with the shaft in that drawing. Even so, it still looks like it's really a geometry problem to solve rather than an engineering design to employ.

[JD Mather]

I strongly suspect that the 45R is essentially concentric with the shaft in that drawing. ....

 

You are right. I remember this problem from back when I used to teach on the drawing board. The R45 is concentric and the rest was all a fudge.

A good example of why we moved to CAD.

I used to assign this when we moved to CAD, but stopped using it because it didn't come out right (as some have found) with the R45 concentric.

A better example of why to use Parametric CAD.

This is the first time I tried it with parametric geometry constraints not making any assumptions that I wasn't sure of (I think it is very safe to assume the assumption that the arcs should be tangent and coicident at the endpoints). I was surprised when the problem solved without needing another dimension or a constraint of the R45 to the origin.

I am going to use this one for classes again - with the warning to not make any assumptions other than those which can be defended as logical.

[welldriller]

You should have dimension tools for linear, aligned, diameter, radius and angle.

I have never used AutoCAD LT, but I am quite sure it has an angle dimension tool.

 

Talk about feeling stupid I do have the aligned command and had never used it. I have learned more on this forum then i did in 12 months at a trade school back in 1980.

[SEANT]

I am going to use this one for classes again - with the warning to not make any assumptions other than those which can be defended as logical.

 

This is a valid lesson. The only logical course of action by the student, however, is to return the assignment with a statement “Ambiguous description: Corrections or more information required.”

 

Many CAD operators will run into poorly laid out projects, and it is important to quickly determine it as such. They should strive to not make assumptions. Get clarification.

[welldriller]

Hi, welldriller. It looks like you substituted diametral dimensions for angular. Have you tried invoking DIMAngular and picking a couple of lines? That should help you get where you want to be in showing angular dimensions.

No i have not -- but you can bet that i will So much knowledge being given and so little head to put it in.

 

Thank you for the information.

[tonyj]

If we assume all of the arcs are tangent and they stop/start at the angles given - there is one solution. (none of the arc centers are on any of the construction lines, but it is fully defined with the given dimensions) (BTW - solution was found in less than 10 minutes.)

 

[ATTACH=CONFIG]41871[/ATTACH]

 

JD,

Are the end points of r61 and r47.3 definitely tangent at where the line intersects? Also you don't show the hole with the key-way. I drew this in Autocad and the key-way finished lower down than was shown in the original drawing. Also, I can't get r61 and r47.3 to be tangent where the line intersects which leads me to say it cannot be done if you are to follow the criteria of, "assume all of the arcs are tangent and they stop/start at the angles given".

[tonyj]

There is no dimensional information provided that indicates the R45 is concentric with the hole for the shaft.

Tangency is not possible all around the cam with a solution that makes that assumption (given that it is an assumption for the R45 to be concentric).

But the two arcs, r45 and r61.0 should be tangental on the line that is running horizontal from the centre of the hole.

Also, may I add to my last reply above, 'I can't get r45 and r61.0 to be tangent when they are intersecting the horizintal line either', it just is not possible to do this.

[tonyj]

JD,

My sincerest apologies. I just saw your drawing on post #32 (I'm an idiot), that is impressive.