Epicycloid and Hypocycloid Curves to design a Lobe Pump.

tog_minusDesign a Lobe Pump with Epitrochoid and Hypotrochoid Curves

You can design a Lobe Pump rotor by combining Epicycloid and Hypocycloid Curves.

The number of lobes is given by the ratio of gear teeth in the Gear Pair. Two and three lobes are very common.

Lobe Pumps are sometimes called Roots Blowers - after the inventor - Roots - and 'Blower' because they were originally designed to pump air.

They are often used to pump liquids with some soft solids....


You must know how to:

Add a 2D-Cam
Export the Cam to SOLIDWORKS
Edit the Cam in SOLIDWORKS
Re-import the Cam into MechDesigner

Steps to design the Roots Blower shown in the video to the left.

1.Add two gear-pairs, one External and one Internal Gear, to Roll around a fixed gear to give a Hypocycloid and an Epicycloid Curve .
2.Make the ratio of the two the same, and so the they start at the same angle.
3.Add a Cam to re-create the Hypocycloid and Epicycloid Curves.
4.Export the cams to SOLIDWORKS.
5.Edit the data to create the solid models. Re-import the Lobes to complete the model.

Details below.


Add a Gear-Pair with an orbiting external gear.

The input is a Crank.

Use these settings:

Mesh = External
Module  = 1
Gear 1 = 180
Gear 2 = 45

See image


Add a second Gear-Pair with an orbiting external gear.

Make the Crank for this Gear-Pair have the same rotation position.

Use these settings:

Mesh = Internal
Module  = 1
Gear 1 = 180
Gear 2 = 45


Edit the Motion-Dimensions for the Cranks.

Make the Base-Value for both to be '0º'.


The image shows the Cranks away from the the horizontal , to show that they more together.


Edit the Geared-Rockers (the Part rotating with the smaller gear) to make its length equal to the Pitch Circle Radius of the small gear.

In this case the Lengths are 22.5mm

Add a Line to the inner Part.

Make the end of the Line at -22.5, 0. That is, the end of the line is at 180º phase to the CAD-Line in the Geared Rocker Part CAD-Line.


Add a Trace-Point to both Geared-Rockers.

They should meet at the same points around the fixed, big gear.

These show the shape of the Two-Lobe Roots Blower.

The shape of the Lobes Roots-Blower changes from the Epicycloid to the Hypocycloid Trace Paths.

How do we make the shape?

I have found it best to add a 2D-Cam to recreate the paths of the Epicycloid and Hypocycloid Trace-Points.


Add a Circle to each of the Geared-Rockers.

Put the centre of each circle at the same Point as the Trace-Points.

You can delete the Trace-Points.

Add a Profile to each of the two Circles.

They can now become Cam-Followers.


Add 2 x 2D-Cams.

Select the Base-Part as the Cam-Part. and the 2 Cam-Followers.

Edit the 2D-Cams - Show only the Pitch-Circle-Path for both 2D-Cams.

The Pitch-Circle-Paths show the same paths as the Trace-Points.

However, you can use MechDeisgner to calculate the points for the Cams, while you cannot calculate the points for the Trace-Points.


Add a Cam-Data dialog-box.

Select the External Epicycloid 2D-Cam.

Calculate as Cam as Arcs option in the Cam-Coordinates dialog-box.


Export the Cams to SOLIDWORKS®.

SOLIDWORKS® shows the Cam profile and the centre point of each arc.


Delete the Arcs that you do not need in this lobe

We only need two external lobes.


Repeat the steps to export the Cam for the Internal Hypocycloid Cam

Delete the Arcs that you not need for this Lobe


At this point you will need to merge the Points at the end of each arc.

Take care not to move the end-points of the Arcs.

To do this, I use the Fix constraint in the sketch editor to fix the point near to the ends where I want to merge the two cams tracks.

Leave one of the Points at the end of one of the Cams so it can move, then merge it with the end Point of the other Cam that has fixed Points.


When both cams are as one loop you can extrude it in SOLIDWORKS.


Then you must add a Coordinate System.


Import the Part to one of the Cranks in the MechDesigner model.


Add a second Crank for the centre of the other Lobe of the Pump.

Make it 180mm from the centre of the Crank used for the Gear-Pair

Use a Gearing FB, and set the Gearing Ratio to -1. This lobe rotates in the opposite direction.

Import the SOLIDWORKS Part on to this Crank also.


This is the basis for the Lobe Pump.

You can add the casing etc.

Normally Lobe Pumps have a simple 1:1 Gear Pair external to the casing, to drive the Lobe shafts.

You can add this if you like.


When you Cycle the model, you can see there is rolling/sliding contact between the Lobes at all points in the machine cycle.


This prevents the fluid leaking back through the centre of the lobes.

In reality there should be some clearance and leakage.

Any leaking is defined by the Volumetric Efficiency of the Pump.

Tutorials and Reference Help Files for MechDesigner and MotionDesigner 14.2 + © Machine, Cam, Mechanism, and Motion Design Software by PSMotion Ltd