National Physical Laboratory

Low Force Measurement

The need for traceable force measurement in micro- and nanotechnology is critical. Any process that operates on the micrometre to nanometre scale will have important forces acting in the low force regime. Materials and technolologies are typically being pushed to their limits, and quantitative force measurement is essential.

For this reason, NPL is continually developing an infrastructure for nanonewton force traceability.


NPL is active in the area of low force metrology. Some examples of work in the area include the development of thrust balances for space propulsion systems operating in the range from 0.1 μN to several millinewtons and the development of artefacts and devices for measuring the spring constant of atomic force microscopes (AFMs). The aim of the work described here is to provide traceable force measurement in the range 1 nN to 10 μN. Beneficiaries of a low force measurement facility include manufacturers of micro-electromechanical systems (MEMS), medical applications (for example, immunoassay devices using MEMS), low force thruster manufacturers and the materials testing industry.

Traditionally, the traceability route for force measurement has always been the force generated by a known mass in a known gravitational field. However, for forces below 10 μN (equivalent to a mass of 1 mg) the uncertainties in weighing are too high and the masses too small to conveniently handle. For such small forces, however, there is the possibility of traceability via electrical and dimensional measurements using specialist balances and MEMS devices.


Low Force BalanceFigure - Low Force balance 

NPL’s recent successes and ongoing developments include examples such as:


The NPL low force facility provides traceability to industry via a two-stage process: an ‘ideal’ nanonewton force measuring instrument, and transfer artefacts to interface conveniently to users’ instruments. Low Force Traceablilty InfrastructureFigure - Low Force Traceablilty Infrastructure 

The ongoing aims of the NMO Programme work in this area are:

  • Evaluate, optimise and maintain the NPL Low Force Balance, taking advantage of new developments in the field
  • Develop a suite of calibration transfer artefact to complete the traceability link and enable fully traceable nanonewton force calibration for industry
  • Participate in international low force comparisons with National Metrology Institutes in the USA, Germany, South Korea, and beyond to support and demonstrate national and international metrology capability and standards

In addition, NPL is always keen to:

  • Explore with users, industry and academia a wide range of applications of its capabilities, and non-standard usage of the low-force facility
  • Proactively develop advances in low force metrology, both for more cost effective measurements in the current range and novel traceability for piconewton forces.

The Low Force Balance

The Low Force Balance, developed in collaboration with TU/e, in the Netherlands, is an electrostatic force balance. It consists of an elastic linear guidance, to which the force to be measured in applied. The resulting displacement is measured with a differential plane mirror interferometer, while a servo control system with an electrostatic actuator drives it back to a null position. The force to be measured is then calculated from the applied voltage. This method allows a very high level of traceability directly back to fundamental physical constants and unit definitions, a key advantage over other approaches. See the schematic below:

Low Force Balance
Figure - Low Force balance schematic

Novel transfer artefacts

Harnessing the latest developments in micro-fabrication techniques, NPL is developing novel MEMS transfer artefacts that can transfer a traceable calibration from the Low Force Balance to a variety of users in industry.

The NPL design combines proven, high-performance MEMS internal displacement sensing technologies with a novel geometry designed to minimise the uncertainties that typically dominate cantilever transfer artefact usage. This work builds upon NPL’s experience in MEMS for micro-coordinate metrology.

Transfer artefact concept sketchFigure - Concept sketch of a low force transfer artefact


Elements of this project are being carried out in partnership with the:


  • Jones C W, Leach R K 2008 Review of low force transfer artefact technologies NPL Report ENG 5
  • Leach R K, Oldfield S, Awan S, Blackburn J, Williams J M 2004 Design of a bi-directional electrostatic actuator for realising nanonewton to micronewton forces NPL Report DEPC-EM-001
  • Leach R K, Oldfield S, Georgakopoulos D 2006 Traceable nanonewton force measurement at the National Physical Laboratory UK Proc. 6th Int. Conf. Euspen, Baden, Austria, 28th May - 1st June 414-417
  • Leach R K, Jones C W 2008 Towards a traceable infrastructure for low force measurements IFIP International Federation for Information Processing, Volume 260, Micro-assembly technologies and applications., Springer, 307-314
  • Henselmans R, Rosielle N, Cacace L, Kappelhof P, Klinkhamer F, Spierdijk H 2004 Low force measurement facility: mechanical design report (Technical University of Eindhoven) – by collaborating group
  • Hughes, E B, Oldfield, S 2004 Thrust balance for ground testing of electric thrusters 4th euspen International Conference, Glasgow, UK, May - June 432-433
Last Updated: 31 May 2013
Created: 7 Jun 2007