Rack and pinion movement problem

[rjsutton]

Hi
I have a problem that i hope someone can help me with
I have 3 items
item C is a fixed plate with a length of 900mm
item B is a plate 900mm long it is connected to C with linear bearings and needs to move a total of 400mm . This happens already by using a linear actuator that is connected to the right side of C and right hand of B. when activated this works perfect to push B out 400mm.
Item A is connected to B with linear bearings. This item needs to move 700mm along the bearing until it is flush with left side of B.
what i need is a solution by using a rack and pinion setup to create this movement
i THINK that if a rack was fixed to right of part c and allowed to slide on the side of B . A pinion would be fixed to the side of A so when b moves the pinion would be forced to turn which would create forward movement in A.
if this works i would need to know the ratio of teeth on the pinion as the rack would move 400mm and part A 700mm
Would appreciate any help ive attached a diag of how i think it should be set up but i may be totally wrong
I could use a linear actuator mounted on B with a 700mm stroke to push A but would rather use some mechanical means
thankyou

 

[hydtools]

A moves 1100mm relative to C. B moves 400mm relative to C. So the relative motion 1100 to 400 would be A to B.
Looks like B needs pinion to a fixed rack on C and A needs a rack driven be the pinion on B.

Ted

 

[rjsutton]

Thanks Ted
If im understanding A and C would have fixed racks with a pinion mounted on B ( catching both racks )
I was thinking of using 2.0 mod track
Any idea on the no of teeth on pinion to convert the 2 different travels.
Thanks

 

[IRstuff]

I don't think you can do that; the teeth per inch on both racks have to be the same with a single pinion. You could have two separate pinions driven by a single shaft, then a ratio of 7:4 in teeth count on the two pinions.

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[hydtools]

You need a double pinion. The smaller one engaging the rack on A and the larger one engaging the rack on C. The larger gear would be 1100/400 the size of the smaller gear.
edit: what I called a double pinion should be called a compound gear pinion. Alternatively you could use a three gear train mounted on B and arranged to speed up C in a 7:4 ratio. The input gear engages rack A, an intermediate gear to change rotation of the output gear engaging rack C.

Ted

 

[capnhook]

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[rjsutton]

Hi capnhook
im 59 and not studying anything. I am making a machine and have a real problem with sorting out a movement problem
thanks

 

[hydtools]

rjsutton, here is one sketch.

and another:

Ted

 

[IRstuff]

I think your pinion ratio should be also 7:4, since A's motion is a combination of its own motion plus B's

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[hydtools]

I don't think so. The pitch circumference of the larger gear must move its rack 1100mm relative to C.
Edit: irstuff, rethinking this I have to agree. A moves 400 with B and another 400 due to the rack movement for a total of 800 relative to C. A needs another 300 displacement. So, 4+3=7 to 4.

Ted

 

[rjsutton]

Guys
thanks for the replies and diags
assume the 2nd diagram is the correct gearing ?7:4
the middle gear is to reverse the rotation direction only
Richard

 

[IRstuff]

Middle gear is the driver, mounted on B. You need to have both driven gears rotating in the same direction

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[hydtools]

In the second sketch the three gears are mounted on B. B moves the gear train. Rack C drives the gear it engages causing the gear chain to transmit drive to the rack attached to A. So C is the input and A is the output.
Change the first sketch by making the ratio 7:4 instead of 11:4 while retaining the idea of a compound pinion.

Ted