Vertical Linear Motion With Rack&Pinion – 1

Linear Guide, Rack&Pinion , Reducer and Servo Motor Sizing for Vertical Motion

Now we have started the calculation of vertical motion. When designing the machine, you need to know that the coefficient of gravitational acceleration will be added to the vertical linear motion calculations.We should also pay more attention to inertia ratio between load and sero motor.

Machine Designing Values;

Max Speed: 500mm/sec

Load : 50kg


The distance between guides and rails is 200mm.

I will start with HSR10 because the weight is very low.When I enter the load and speed values mentioned above, I see that the product is suitable.The most important point to be considered here is the distance of the gravity point distance from the rail’s axis line (100mm).

When choosing servo, we first need to know the pinion diameter. I made the choice of MOD: 1.5 rack and pinion considering the load.The diameter of the Z:20 pinion is 30mm.

Accelaration Time : 0,1sec

Reducer Ratio : 10

As a result, 0.4 Kw 3000 rpm servo motor is suitable for this job.Again, I do not describe the selection of the reducer to be used with this servo motor. I will add this to the subject later on.

Now let’s check the pinion tooth force.


Load: 50kg

Vertical Force at Acc/Dcc




FN for Z:20 = 668N

490*1,2=588N (1,2 Safety Factor)


✔ (in Safe)

Selection results;

Servo motor : SGMJV-0 ( 0,4 Kw low inertia )

Pinion : Straight Mod:1,5 Z: 20 (16MnCr5 DIN 1.7131 Hardened HRC60 )

Rack : Straight Mod:1,5 L:1000mm  ( Cold formed C45 )

Linear Guide : THK HSR10 ( Narrow or Wide type

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