Mechanical Advantage of Rack and Pinion
Mechanical Advantage of Rack and Pinion
(OP)
Hi All,
Can anyone tell me how to calculate the Mechanical advantage of the rack and pinion system. Thank You.
Can anyone tell me how to calculate the Mechanical advantage of the rack and pinion system. Thank You.





RE: Mechanical Advantage of Rack and Pinion
I don't think you can really say there is a mechanical advantage without considering input force. Otherwise, it is a conversion of torque to/from linear force like a lever arm.
RE: Mechanical Advantage of Rack and Pinion
RE: Mechanical Advantage of Rack and Pinion
Friction etc keeps the force in/out ratio being the same.
RE: Mechanical Advantage of Rack and Pinion
No pi in the torque/force equation. Just moment arm, or 1/2 of pitch diameter for the pinion:
Torque = Force * (Pitch dia.) /2
RE: Mechanical Advantage of Rack and Pinion
RE: Mechanical Advantage of Rack and Pinion
If you are more specific about your system, we can probably get you to a more useful answer.
RE: Mechanical Advantage of Rack and Pinion
However, if you read this, you can determine a figure of merit based on the motion of the wheels relative to the sterring wheel. http://www.carbibles.com/steering_bible.html
TTFN

FAQ731-376: Eng-Tips.com Forum Policies
Need help writing a question or understanding a reply? forum1529: Translation Assistance for Engineers
RE: Mechanical Advantage of Rack and Pinion
RE: Mechanical Advantage of Rack and Pinion
What color is a 3-sided square?
RE: Mechanical Advantage of Rack and Pinion
No pi in the torque/force equation. Just moment arm, or 1/2 of pitch diameter for the pinion:
Torque = Force * (Pitch dia.) /2
sorry for not including units to my equation which is correct for his rack/pinion question.....
I was not giving Torque = distance * force
I gave torque= force(#)*pitch (in/rev)/ 2pi (radians/rev).... this converts his thrust force applied to the linear rack into #-in torque on his pinion. there are of course 2*pi radians per revolution so yes pi is included to convert units properly.
RE: Mechanical Advantage of Rack and Pinion
why not tell us what 'mechanical advantage' means to u? it makes no sense in an engineering question as stated.
but if you are trying to find out something to do with torque vs force relationship and how it changes with 'spacing of teeth,' THAT is easy to answer: none. distance between teeth on rack has ZERO bearing on torque vs. force. NOne. zip, zilch. see my equation in previous post - that shows ALL the relationship there is between these two terms.
RE: Mechanical Advantage of Rack and Pinion
Compared to what?
You mean a rack and pinion steering system, right?
You rotate steering wheel A, which has gear B. This translates rack C. The rack connects through a linkage, to driving wheel D, some distance from the wheel's pivot point. As an engineer, you should have no problem figuring out how many turns of the steering wheel are required to achieve an angle of rotation of the driving wheel, and what parameters would affect this.
--
JHG
RE: Mechanical Advantage of Rack and Pinion
TTFN

FAQ731-376: Eng-Tips.com Forum Policies
Need help writing a question or understanding a reply? forum1529: Translation Assistance for Engineers
RE: Mechanical Advantage of Rack and Pinion
Sorry for the confusion. Let me explain clearly what I mean my mechanical advantage.
I need a torque of 100 lb-in at the center of the pinion. I can get an input force of 25lbs from the power source (not more than that) and I can only use 4" dia pinion (limited by space). Therefore I was wondering if there is a way I can choose the a rack and pinion system such that the torque at the center of the pinion will be 100 lb-in. Hope this explation makes my question understandable. Thank you all for the replies.
Regards
Addy
RE: Mechanical Advantage of Rack and Pinion
Is this for school?
TTFN

FAQ731-376: Eng-Tips.com Forum Policies
Need help writing a question or understanding a reply? forum1529: Translation Assistance for Engineers
RE: Mechanical Advantage of Rack and Pinion
You see, on Krypton, physics has different properties than here. There, T=F*pitch/pi, so T=25#*2*pi*2in/pi=100#
But in order to have their physics work, Krypton rock is deadly to their people and causes the same 100# to act like 5# in our universe.... Nothing is totally free.
RE: Mechanical Advantage of Rack and Pinion
If your pinion must produce a torque of 100lb.in, the torque input through your steering wheel must be 100lb.in. what you ought to be looking for the force to move your rack. For a given force, you can reduce pinion torque by using a smaller pinion. The only other way to reduce pinion torque is to put a gear reducer between your steering wheel and pinion.
Are you sure you know what you are doing? Unless I am horribly misinterpreting your question, this is very basic mechanics of machines.
--
JHG
RE: Mechanical Advantage of Rack and Pinion
The torque at the pinion gear radius is 2 inch x 25 pounds equals 50 inch-lbs. The torque at 1 inch radius is 100 inch-lbs. And at zero radius, the formula would be 50 inch-lbs times (2 inch radius divided by 0 radius).
T1 = T x R/R1 where T and R are 50 inch-lbs and 2 inch radius respectively.
Help us determine what you are trying to solve. If a motor was rated at 100 inch-lbs, the force on the rack would be 100 inch-lbs divided by the pinion radius. Is this what you are trying to solve?
RE: Mechanical Advantage of Rack and Pinion
According to the OP, the input torque is 100lb.in. The torque output is not affected by radii. The output force is.
--
JHG
RE: Mechanical Advantage of Rack and Pinion
When talking about the desired torque, is it the input or the output? In other words, are you applying a linear force to the rack and wanting an output torque at the pinion, or are you applying a torque to the pinion and wanting an output force at the rack?
You mention your limitation of a 4" diameter pinion. One thing you need to consider, is the pitch diameter of the pinion. The pitch diameter of the pinion will be less than the OD of the pinion.
Either way, if considering a "friction wheel" (where you could actually have no slippage - not real world) situation where you acutally have a 4" pinion surface moving a rack, you would actually have mechanical disadvantage since you would need to divide the input torque by the pinion radius. The only way you will have an advantage is if you applied the input force to the rack to get an output torque at the pinion.
This made me start thinking about arbor presses which depend on how hard you can pull on the handle which then made me realize why I did a favor and made a new handle for the one we have at work because someone put a cheater pipe on it and bent the original one. :)
Kyle