Development of a 3-axis Force Sensor Based on HBM Strain Gauges

How can a passive and cost-optimized sensory foot for load-bearing walking robots be developed? This research question was approached as part of a robotics project of the Simulation, System Optimization and Robotics Department of the Technical University of Darmstadt.

With the help of HBM strain gauges for transducers a 3-axis force sensor was developed to regulate the motion control of the robot.


Development of a passive sensorial foot for load-bearing walking robots that is more cost-effective than the sensors available on the market.



Based on HBM strain gauges for transducers a 3-axis force sensor was developed to regulate the motion control of the load-bearing walking robots. Due to a pre-coated adhesive layer, the processing of the strain gauges was not only very easy and process-optimized, but also delivered very good results.



12 HBM strain gauges for transducers were connected to full bridges to measure even the smallest resistance change. The considerable results of the first test run will be further optimized in a consecutive project.

The Setup of the 3-axis Force Sensor

The 3-axis force sensor is based on an aluminium feather-spring component in a cylindric beam-structure. This setup is easy to produce and cost-effective.

To measure the forces in x, y, and z direction, three strain gauge full bridges were installed: 

  • Measuring the z direction: Four transducer strain gauge rosettes K-TA11K3/350 were installed inside the feather-spring component with a cold curing two-component adhesive.
  • Measuring the x  and y direction: Eight transducer strain gauges K-LU13K1.6/350 were attached outside of the feather-spring component. Due to the stick-on design the transducer strain gauges could be applied hot and user-friendly.

The strain gauges are arranged like demonstrated in the figure 1. Strain gauges number 1-4 measure the z direction, strain gauges 5-12 measure the x and y direction. 

To measure even the smallest resistance changes, the strain gauges were connected to full bridges (please see figure 2). Thus, it is possible to display the bridge deflection. With the help of ANSYS Workbench 19.1 the qualitative strain of the strain gauges was determined for the specified force direction.

The Test Run of the Prototype

To verify the 3-axis force sensor, a prototype was developed. This prototype was evaluated and calibrated in a first test run. With the help of the calibration devices, the spring body is loaded one after the other in the three force directions.

The calibration conditions for the input and output were as follows: 

Zero signal x-channel (mV)11.42
Zero signal y-channel (mV)5.13
Zero signal z-channel (mV)-28.90
Power supply voltage (DC current in V)3.3
Measuring Range (V)+/- 0.156
Gain factor x-channel 16
Gain factor y-channel16
Gain factor z-channel16

The Results of the Test Run

The calibrated measurement curves are shown in the orange, green and black graphs. As a comparison value, the reference force measurement is also shown in the blue graphs.


Mean absolute deviation from the reference sensor and average relative error:

Force directionMean absolute deviation (N)Average relative error (%)
Fxapprox. 3approx. 1.5
Fyapprox. 4approx. 2.6
Fzapprox. 23approx. 3.1


The results of the first test run clearly show that considerable results have already been achieved with HBM standard strain gauges. To further optimize the results of the mean absolute deviation and the mean relative error, a follow-up project is being conducted at the Technical University of Darmstadt.  

About the Technical University of Darmstadt

The Technical University of Darmstadt is one of the leading technical universities in Germany with high international visibility and reputation. Since its foundation in 1877, the TU Darmstadt has been characterized by a special pioneering spirit. Through outstanding achievements in research, TU Darmstadt opens up important scientific fields of the future. 

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