The Rack and Pinion Constraint block represents a kinematic constraint between a translating rack body and a rotating pinion body. The base frame port identifies the connection frame on the pinion body and the follower frame port identifies the connection frame on the rack body. The pinion rotation axis and the rack translation axis coincide with the frame z-axes.

The block represents only the kinematic constraint characteristic to a rack-and-pinion system. Gear inertia and geometry are solid properties that you must specify using solid blocks. The gear constraint model is ideal. Backlash and gear losses due to Coulomb and viscous friction between teeth are ignored. You can, however, model viscous friction at joints by specifying damping coefficients in the joint blocks.


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The rack-and-pinion constraint is parameterized in terms of the dimensions of the pinion pitch circle. The pitch circle is an imaginary circle concentric with the pinion body and tangent to the tooth contact point. The pitch radius, labeled RB in the figure, is the radius that the pinion would have if it was reduced to a friction cylinder in contact with a brick approximation of the rack.

Gear constraints occur in closed kinematic loops. The figure shows the closed-loop topology of a simple rack-and-pinion model. Joint blocks connect the rack and pinion bodies to a common fixture or carrier, defining the maximum degrees of freedom between them. A Rack and Pinion Constraint block connects the rack and pinion bodies.

The block imposes special restrictions on the relative positions and orientations of the gear connection frames. The restrictions ensure that the gears assemble only at distances and angles suitable for meshing. The block enforces the restrictions during model assembly, when it first attempts to place the gears in mesh, but relies on the remainder of the model to keep the gears in mesh during simulation.

The distance between the base and follower frame origins along the follower frame y-axis must equal the pinion radius. This constraint ensures that the pitch point of the rack is at the proper distance from the rotation axis of the pinion.

The x-axis of the follower frame must be perpendicular to the xy plane of the base frame. This constraint ensures that the rack and pinion are coplanar, and therefore that their motion axes are perpendicular to each other.

If you install the plugin, you can create true involute gears and a mating rack to go with it. As has been pointed out, you can also create them using only native tools, but you specifically asked for an extension.

Not sure if you got your model figured out or not, but even if you have, this may help others in the future. Especially those having trouble wrapping their head around all the math involved in figuring out involute gears.

Initially, I was going to use an extension to build my rack and Pinion and even installed and tried one, but it was more confusing than helpful, and I wanted to get hands on and learn it my way, because as you can see, my pinion is a bit unique in this design.

Anyways, the trick was working with only two components, which were half a tooth from the pinion and half tooth from the rack, which were aligned along the pitch line, or pitch radius, For the pinion, I first drew a circle and cut an 18 slice of pie out of it, which is half of 36. A full tooth is 36 in my design, because I have 10 teeth.

TRIAC pneumatic rack and pinion actuators are designed and manufactured to provide the highest cycle-life on the market. We can accessorize them to accomplish virtually any control requirement. They are available with various mounting dimension configurations and span eleven models for appropriate torque compatibility.

I'm trying to model a special type on rack and pinion gear system where what is special is that the rack in not linear but circular(bigger rides on a circle off center from the pinion gear and much bigger than the pinion gear diameter pitch)

and I'm having problems with calculating the ration(in degrees) for the motion link between the rack and pinnion for confirming the model is right maybe I've got the pitch distance for the rack in the "pattern along path" wrong as well.

The spacing in the rack pattern was correct, but you used the outside diameter of the tooth as the path, instead of the construction diameter - for want of a better description. I think it is PCD but not sure on that. Updated that.

I am also looking for designing a similar type of circular rack and pinion system where circular rack will be driving the pinion. I want to know how to calculate gear ratio for this system, and whether it can have a gear ratio of 50:1 or above?? Can someone please help me out. Thanking in advance

The Rack & Pinion block represents rack and pinion gear that converts between translational and rotational motion. The rotational-translational gear constrains the pinion (P) and rack (R) to, respectively, rotate and translate together in a fixed ratio that you specify. You can choose whether the rack axis translates in a positive or negative direction, as the pinion rotates in a positive direction, by using the Rack direction parameter.

There are a lot of YouTube videos and Community posts on this subject. Try searching to see if there is something that already answers your modeling questions. There are crude but quick models and more precise but more difficult ones. I believe someone uploaded a parametric involute gear model.

Otherwise, to better understand, why do you want to? Gears are typically formed on very precise machinery and there is rarely a CAD model that is used to define them. Particularly for involute gearing, the parts are typically described only by a chart of relevant parameters for the gear teeth. Prior to CAD, gears were only shown on drawings with a circle to represent the pitch diameter and a circle to represent the OD.

To solve that particular problem you need to pick a gear that is smaller than the gap and still have room for the rack gears. There is no method to do this because there are an infinite number of solutions. You can look at gear catalogs to see what parts are commonly available and see what fits.

I am currently working on a mechanical flower where I will use a linear motion to create a radial motion from 0 to 90 degrees. The linear motion will be 40mm from a crankshaft and I am now having problems designing the rack and pinion. Is there any easy way to calculate or think about how the degrees and distances should be between the gears? I have done some research but have not found an easy way to calculate it and I would like some input on my current design. Right now I have the problem that the further the pinion moves upwards the more problems I get (see pictures). I would highly appreciate any help with this problem!

If you need to actually model gear teeth, then you need to go to a machine design reference to get the theory and equations behind the tooth profiles etc. Unless you will be manufacturing these parts yourself, this may not be necessary. I have designed entire gearboxes and built them without modeling a single tooth profile. Using purchased gear components will enable you to skip the modeling of gear teeth.

This entire gearbox for a harmonic balancer was designed in Creo and I did not model any of the teeth. I did the kinematic and dynamic analysis in Creo mechanism design confirmed with some hand calculations and then bought gear pairs etc. off the shelf. The design was validated in a test stand and eventually went through a successful flight test protocol.

I am guessing from your "sketched" gear that you need to learn and apply gear theory concepts such as module / pitch / gear ratios and also involute curves and pressure angles. Searching for "rack and pinion mathematics" returns a bunch of resources, for example:

The EL-O-Matic F-series is a rack & pinion actuator, available in 13 sizes as spring return or double acting models. The actuator's Fit & Forget design provides the optimum performance for a wide range of quarter turn valve applications. The EL-O-matic F-series are powder coated and comes with a special high corrosion resistant aluminum pinion design and stainless steel fasteners, resulting in a long lasting durable actuator design.

A rack and pinion is a type of linear actuator that comprises a circular gear (the pinion) engaging a linear gear (the rack). Together, they convert between rotational motion and linear motion. Rotating the pinion causes the rack to be driven in a line. Conversely, moving the rack linearly will cause the pinion to rotate. A rack-and-pinion drive can use both straight and helical gears. Though some suggest helical gears are quieter in operation, no hard evidence supports this theory. Helical racks, while being more affordable, have proven to increase side torque on the datums, increasing operating temperature leading to premature wear. Straight racks require a lower driving force and offer increased torque and speed per fraction of gear ratio which allows lower operating temperature and lessens viscal friction and energy use. The maximum force that can be transmitted in a rack-and-pinion mechanism is determined by the torque on the pinion and its size, or, conversely, by the force on the rack and the size of the pinion. 2351a5e196

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