Rotary to Linear Motion

[rkukl 0]

Any Ideas

[BobLfoot 301]

I am not a motion guru - Peter Natch... comes to mind. But here goes. If you have a rotary encoder on the cam wheel then a cam profile should be able to adjust desired speed based on where in the rotation you are. For example going from 12 o'clock to 2 o'clock produces less linear motion then 2 o'clock to 3 o'clock and 3 o'clock is a reversal point where you need a ramp down/ramp up as you approach and leave it.

[atanas 0]

Hi rkukl, I do not think you could achieve linear motion with this mechanism with ramp up/down. you might look at this site for the speed formula: http://www.wfu.edu/~rollins/piston/ I would suggest using different mechanism (Rack and Pinion). You would have to add adjustable limit switches and perhaps a gearbox and do some programming. Regards, Atanas Edited 23 Mar 2009 by atanas

[Peter Nachtwey 15]

Nice link, it saves me from having to do a little work. However, the real problem is that rkukl needs to know the angle, the radians per second or RPM and the rate of change of RPM as a function of position, velocity and acceleration. Calculating that will be messy on a PLC without a motion controller card. Other simple solutions have be presented on plcs.net. We must wait and see if rkukl needs the precise answer and is willing to do the calculations to get the precise answers.

[paulengr 44]

Not linear. If you add 1 link to get what looks like the classic "steam piston to rotary" motion that you'd see in any model of a steam locomotive for instance, you'd get approximately rotary but the acceleration/deceleration is effectively close to a sin function. Need at least a 4-link system (and probably 5-link) to get reasonably close to linearity with just a cam and link system. Rack-and-pinion gets you to linear in 1 step. So do linear actuators (pneumatic, hydraulic, or variants of the linear motor variety) and/or ball/roller screws. Any reasonably good book on engineering mechanics will explain these various types of systems and the advantages and disadvantages of each one.

[Peter Nachtwey 15]

Linear systems have been suggest on plcs.net. Linear mechanics are the way to go. The fact that rkukl's system is non-linear wouldn't be a problem if the equation can be 'inverted' so that angle, angular velocity and angular acceleration can be expressed in terms of linear position, velocity and acceleration. The link ideas would be mechanical nightmares.

[Peter Nachtwey 15]

BTW, I was interested in calculating the inverse kinematics formula. I have the one for position only right now. It is messy like I thought it would be. The formula for computing the angle as a function of the position is theta=atan2((r^2+s^2-b^2)/s*r ,+ or - sqrt(-(r+s+b)*(r+s-b)*(-r+s-b)*(b-r+s))/rs); I am sure the formula for theta' and theta'' ( omega and omega') are even more fun. I haven't worked on those. However once I have them then I can move a virtual axis back and forth as if it was a normal linear linear axis. I would then use the position, velocity and acceleration generated an angle, theta and its first and second derivatives every 10 milliseconds. We have a function that uses these values as parameters and computes a nice quintic curve between the angles. The rotary motion is then converted into a nice linear looking motion at the object or piston. This is much more than what can be done in a PLC. The control logix doesn't have the motion commands to do the 5th order polynomials on-the-fly. I am sure rkukl is looking for much simpler mechanical solutions right now.

[Steve Bailey 118]

Actually, I think RKUKL is looking for a simple, PLC-based solution to implement an improvement in his finished product. Over at PLCTalk.net he indicated that the mechanism moves a rewind reel back and forth as product builds up. Due to the geometry of the mechanism, the traverse speed is slowest as the reel reverses direction. The slowdown leads to a buildup of material at the edges of the reel. He would like to increase the speed of the motor that drives the cam so that the reel takes less time to reverse direction. He's not looking for a perfectly constant traverse speed with the fastest possible reversal. He just needs to be able to reverse without building up as much material at the edges. I'm also pretty sure that his boss isn't going to fund a complete mechanical rework. I think he's trying to convince the boss that there will be some improvement by adding a VFD to change the motor speed. If he can make a convincing enough case, his boss may approve buying the VFD. RKUKL, forgive me if I'm putting words in your mouth.

[jimdi4 2]

This sounds allot like a TrimPress opeation, something you would find in the plastics industry maybe not quit exactly the same but very similar. On a trim press the driving force is an AC motor driving a gearbox. Of course I'm talking about a much larger machine perhaps, but the physics are there. When I worked on these machines the only PLC control was for monitoring and starting up the motor. The machine was built strickly as a mecahnical device. Occasionaly there was questional electrical problems with the machine however 99.9% of the time it was proven to be a mechanical issue such as a misdajusted part, or gearbox issue. I actaully monitored the current on the flywheel as the trimpress was running and it strianed going up (pulled allot of amps) and comming down. Both motions made the motor work harder but the speed of the press never changed. Here is another link for Engineering formulas: http://www.engineersedge.com/calculators.htm Edited 24 Mar 2009 by jimdi4

[pandersen 0]

Could you use a cam profile to do the transformation?

[Peter Nachtwey 15]

Yes, a cam table can be made now that there is a formula to convert the objects position, s, into angle. Now one would make linear moves on a virtual axis and use the position to index into the cam table to calculate the rotary angle. The cam table would probably provide a good enough estimate of the rate of rotation and its derivative too. This is important for calculating feed forwards. Better controllers can do this calculation without a cam table and do it on-the-fly. This provides extra precision since most controllers cam tables only provide 3rd order interpolation but that would probably good enough for this application. A Control Logix can probably do this application IF there isn't an need for precision and rkukl wants to spend the time figuring it out.