Design Considerations to Convert Rotary Motion into Linear Motion


A standard electrical mini motor generates rotary movement but in many applications the load moves linearly instead of rotationally. This is typical for medical pipettes or syringes, mesotherapy devices and pick and place machines for industrial markets and fluid regulation valves. Engineers must develop their own system to translate rotatory motion into linear motion.

The main area of focus should be on the development of the core product. The selection of the miniature motor and the design of the transmission system should be provided by motion specialists in order to save precious development time. Let’s take a closer look at the linear motion possibilities.

Rotation can be converted into linear motion via a screw and nut system assembled on the motor shaft. There are 2 main types of screw and nut systems:

  • A Ball Screw (see figure 1) operates on rolling contact between the nut and a screw. The ball is recirculated along a helical groove. Due to the rolling components, this solution has very low friction, allowing high efficiency (greater than 90%) and a high load capability.
  • A Lead Screw (see figure 2) is composed of a screw (generally in stainless steel) and a nut (generally in plastic). Both components are in direct contact which generates more friction than the ball screw. However, this option is a good, economical solution when cost is a key consideration. The material of the nut generally affects the life and maximum load capability of the assembly. However, with 2 preloaded nuts, the axial play can be eliminated.

There are typically two types of linear solutions to consider:

  • Option 1: The lead screw is directly integrated into the motor
  • Option 2: The lead screw is mounted on the motor shaft

Option 1: Motor with Integrated Lead Screw

Standard linear actuators (often called digital linear actuators, or DLA) are a fully integrated linear solution utilizing a can stack stepper motor. This is generally a cost-effective solution. Inherent with stepper technology, the motor is a positioning system by itself, so the control does not need position feedback. The DLA can be driven in full steps, half steps or micro steps, depending on the resolution desired. Another benefit is the detent torque from the motor allows the DLA to hold its position with power removed.

For the linear transmission, a nut is over-molded in the rotor assembly (see figure 3) with a special material optimizing the friction, resulting in an efficient solution and long lifetime.

Some products even have a special ball bearing assembly, where the ball bearings are pre-loaded with a wavy washer to reduce the axial play (see figure 3). This improves the linear positioning accuracy, as well as the repeatability of motion. The lead screw extends and retracts during motion, with the ability to return to the same starting position if desired.

When considering the right linear motion solution, you want to also take into consideration some options generally available as a standard for optimizing the solution:

  • Stroke length
  • Lead screw pitches (generally 2 or 3 choices / references)
  • Coil type: bipolar or unipolar
  • Coil rated voltage
  • Rated current
  • Captive lead screw (anti-rotation integrated) or non-captive lead screw (see figure 4)
  • Various thread tip available in metric and imperial

Linear Actuators can be a very cost-effective solution, providing high linear force and reliability for your machine.

Option 2: Custom Motor Solution

For applications requiring high performances in a limited package, it’s recommended to consider a solution that can be customized. Custom-made solutions are usually built with either a brush DC, brushless DC or stepper disc magnet motor. These technologies offer different benefits and advantages over can stack steppers. As an example, for high acceleration applications we recommend using a low inertia motor such as a disc magnet stepper. For high power in a small package, a combination brushless DC, gearbox and lead screw can be the best solution. And for high efficiency, a coreless brush DC motor can be the best solution, especially for battery powered applications. Some accessories can also be mounted on the motors such as an encoder for high resolution positioning feedback.

A custom-made solution also provides flexibility around the lead screw selection. The R&D team can choose if it is better to have a ball screw or a regular lead screw, suggest different pitches, adapt the material or even optimize the dimensions.

To design a motorized assembly, it is important to understand both the power required from the application and the power generated at the motor level. There are some physical relations to convert the desired output force and linear speed into the required input torque, as well as the rotative speed. Let’s explore some examples of how to determine the optimum solution to help you achieve your application’s required output.

Example 1: Digital Linear Actuator

Application description

A team is developing a laboratory medical device which moves a tiny amount of liquid in tests tubes. One motor controls a multi-pipette channel. The motor package is limited to a maximum diameter of 20 mm. It is important to have good repeatability and accuracy to consistently provide the same amount of liquid with each operation.

The working process can be divided into two main steps:

➞ Step 1: Fill the pipettes in 1 step in less than 4 seconds.

  • Travelled distance of the pipette: 50 mm in 4 sec. Speed = 12.5mm/ sec
  • Force 20N for a viscous liquid

➞ Step 2: Empty the pipettes. The pipette content is divided into tiny amounts for several test tubes.

  • Travelled distance: the pipette must be able to divide the volume into 30 sub steps, i.e. 50mm / 30 = 1.6mm
  • Force 15N


Digital linear actuators are typically a good solution for this type of device because:

‣ The solution is usually available as a standard with no development required

‣ Due to the stepper technology, it is easy to control the liquid delivery into sub-volumes

‣ Thanks to the preloaded ball bearing assembly, there is no axial play in the DLA, allowing good repeatability

To select a motor, we recommend the following process. The example is illustrated with the motor 20DBM supplied by Portescap, see figure 5:

  • Dimension – remove solution with diameter > 20mm ( 1 )
  • Stroke length – The travelled distance is 50 mm, so the minimum stroke length is 50 mm. The captive version can be removed as the stroke length is smaller than 50 mm. ( 2 )
  • Power - Check if the motor can work at the required force. ( 3 )
  • Calculate the frequency necessary to reach the targeted linear speed. The frequency depends on the lead screw pitch. Refer to column 3 and 5 in Table 1. ( 4 )

Consult the pull-in force graph to select the screw pitch. Refer to column 4 in Table 1. ( 5 )

  • Coil – It’s important to choose a coil which is adapted to the power supply. A coil with low number of turns has a low resistance and is appropriate for a power supply type of high current, low voltage. A coil with a high number of turns has a high resistance, and it is appropriate for a power supply type of low current, high voltage. ( 6 )

‣ Taking into account the parameters and performances of the above example, this motor with the screw 10 would be a good option.

Example 2: Custom Motor Solution

Application description

Another engineering team is now developing a medical device which will be handled by the doctor during an operation. They work with the following requirements:

The tool will be handled by a doctor and it will be battery powered for better ergonomics. The engineer can only accommodate a solution with a maximum diameter of 13 mm, and the tool must be optimized in order to have a good efficiency.

The typical power requirements are the following, see table 2:

 Force (N)
 Speed (mm/s)
 Mechanical Power needed (W)

Table 2. Power requirements

Power calculation

As the solution is battery powered, the coreless brush DC motors are a good technology to reach high efficiency. The power requested by the motor can be estimated by assuming a gearbox efficiency of 75% and a lead screw efficiency of 50%, which give a power of 1.87 W.

Power Calc

By calculating the estimated power, we can identify the typical size of the motor. For this example, we can confirm that a small diameter motor can do the job.

Conversion of linear speed / force into rotative speed / torque

As the motor produces a rotative motion, we need to convert the linear speed into rotative speed and the force into torque. The conversion depends on the lead screw which is specified by its lead.

Physical relations

If the screw (mounted on the shaft) rotates 1 round (2 π), the nut moves linearly on a distance equal to the lead (see figure 6).

Consequently, we have the following relation, allowing to convert linear speed into rotative speed:

In looking at the power relation, we can deduce the force/torque relation:

The physical conversion formula can be applied in the example. As the torque and speed depend on the lead screw, we can calculate with two different leads to understand the impact of the lead selection.

Note: The lead screw lead impacts the efficiency, as the efficiency is related to the friction of the material and the screw angle.

The previous relations are now used in the example, see Table 3.

A smaller lead requires higher speed and lower torque than the larger lead. In general, the smaller lead also requires more power due to the lower efficiency.

Gearbox selection

The gearbox selection depends on the output torque and on the input speed.

The Portescap catalog indicates the gearbox R13 can be a potential solution working with both screws. This gearbox has a maximum output torque of 0.25Nm (> the calculated torque). The maximum input speed of this gearbox is 7500 RPM.

Ratio selection

Thanks to the maximum recommended input speed of the gearbox, we can define which maximum ratio to choose.

To define the maximum ratio, we divide the maximum input speed by the output working speed, and compare it with the ratio available, see table 4.

*We generally choose the closest and smallest ratio available in order to have a working input speed lower than the recommended maximum input speed.

Motor selection

To choose the motor, we need to calculate the application input torque of the gearbox. As this is a continuous application, the motor must have a maximum continuous torque higher than the application gearbox input torque, see table 5.

For both screws, we can use the motor 12G88 which has a maximum continuous torque of 3.5 mNm.

Solution selection

The electrical power, efficiency and solution dimension can now be calculated for each solution, see Table 6.

The 12G88 215E has the following specs:

‣ torque constant k = 4.9mNm/A

‣ resistance R = 3.2 Ω

Technically, both solutions can work but depending on the requirements of the application you may select either option 1 or option 2. As an example, if the goal is to prioritize the battery life compared to the solution package, then option 2 seems to be the best. Indeed, the total efficiency is 30% whereas option 1 is only 18%. The drawback of option 2 is the size because gearbox 2 has 1 more stage than option 1, consequently this solution is 3g heavier and 3.1 mm longer.


For linear applications, motor suppliers can support the development team by offering standard linear motors or by developing a linear, custom motorized solution. For both parties (motor supplier and application designer), it is important to define the technical requirements in the device but also at the motor level. For any development, the key is to have a full understanding of the project’s needs, in order to find the best compromise between technical and commercial requirements.


Figure 1
Figure 1: Ball Screw
Figure 2
Figure 2: Lead Screw
Figure 3 Cutaway Line Drawing
Figure 3: Example of a Can Stack Linear Actuator with Zero Axial Play
Captive vs Non-Captive Design
Figure 4: Captive vs Non-Captive Design
Table 1
Table 1. Selection of the 20DBM Screw Lead
Figure 5 Design Consideration Linear Motion
Figure 5: Linear Actuator Selection Process
Motor and Lead Screw
Figure 6: Motor and Lead Screw
Table 3
Table 3: Calculation of the Linear Speed and Torque Depending on the Lead Screw
Table 4
Table 4. Gearbox Ratio Selection
Calculation of the Torque at the Motor Level
Table 5. Calculation of the Torque at the Motor Level
Table 6
Table 6. Power Calculations for each Solution