Beam theory: Buckling

Introduction For slender structures there is a risk that buckling can occur when they are loaded on axial compression. This sheet gives an overview of the force at which buckling occurs ($F_b$) for beams constrained in various ways. The buckling force is given by: $$F_b=frac{pi^2EI_x}{L_b^2}$$ With $L_b$ the buckling length of the beam given by […]

Preferred fits

Preferred fits The table below shows the preferred fits according to ANSI B4.2-1978 with its overlap with the preferred fits of ISO 286-1 (2010) marked in green. Fits on shaft basis are preferred because of the availability of h6 dowel pins. For precision mechanisms G7/h6 is generally used as H7/h6 has a risk of getting […]

Static balancing

Introduction Statically balanced mechanisms are used to compensate for the gravity force of masses. Allowing these mechanisms to move from one configuration to another without the need for large actuation forces. This gravity compensation is done by using springs. Static equilibrity equation To have a static equilibrium the sum of all forces has to be […]

Beam theory: Stiffness of combined loads

Introduction Most beam theory examples use perfect loading conditions with often a single load. But what happens when the loads are not applied at the perfect location or when a combination of loads is applied? This page aims to give some feel for the change in stiffness by giving two examples; tension/compression combined with bending […]

PiezoKnob: Actuation based on inertia and stick-slip

Introduction The PiezoKnob is a stepping actuator with nanometer level resolution which, when powered down, combines a high holding force with sub-nanometer stability. This is of particular interest for high precision equipment operated in vacuum and cryogenic environments where heat cannot be removed by convection and cooling power is typically limited. The inertia & stick-slip […]

Force sensor design: Example

Introduction A force sensor can be obtained from a well-matched combination of a known stiffness and a displacement or strain sensor. Typically commercially available force sensors have been designed for high stiffness (> 1e6 N/m) to measure large forces (>> 10 N) which makes them unsuitable for applications requiring mN or even sub-mN resoluti0n. For […]

Cryogenic positioning stage: High resonance

Introduction This XYZ positioning stage is specifically developed for cryogenic applications where high resonance frequencies are required. Furthermore this stage can be used in a scanning mode for small movements around a given set point. Pro’s & Con’s Operational down to 1 K High resonance frequency Sub nanometer resolution scanning mode Play/backlash free Antimagnetic materials […]

Third order point-to-point motion profile

Introduction In many mechatronic applications where a movement from A to B needs to be performed, a third order point to point motion profile is used.To enable early insight in the relevant parameters of a motion profile it is useful to calculate and visualize the relevant parameters (position, speed, acceleration and jerk). This sheet provides […]

Structural damping properties of mechanical systems

Introduction Each mechanical system from actuator to end-effector comprises damping. This sheet provides some insight how to predict this damping. Damping depends on many factors, such as material, shape, environment, velocity, etc. and therefore it is difficult to predict. Sub- super- and critical damping A critically damped system converges as fast as possible without oscillating […]

Structural damping definitions

Introduction Every part of a mechanical system, from actuator to end-effector, comprises damping. This sheet gives an overview of ways damping can be defined and how these definitions are related to the linear dimensionless damping coefficient $zeta$. What is damping? Damping in mechanical systems is the extraction of mechanical energy from the motion in the […]