Displacement sensors: Concept overview
Introduction Displacement sensors can measure distance or displacement in various physical ways, such as: Resistive Capacitive Inductive Piezo effect Electromagnetic Optical This sheet displays these physical working principles and shows the advantages and disadvantages of these principles, along with some typical parameters such as resolution and range. It is very useful if you are to […]
Displacement sensors: Parameter definitions
Introduction Evaluating sensor specifications can be confusing. Part of this is due to the ambiguous parameter definition which varies between mechanical and electrical engineers and from manufacturer to manufacturer. Below the unambiguous JPE-definitions. Displacement versus Position A position sensor measures with respect to a defined zero and it does not require a homing procedure. A […]
Temperature sensors & read out: Parameter definitions
Introduction Evaluating sensor specifications can be confusing. Part of this is due to the ambiguous parameter definition which varies between mechanical and electrical engineers and from manufacturer to manufacturer. Below the unambiguous JPE-definitions. NOTE: Temperature scale can either be in Kelvin or in degree Celsius. Only Kelvin is used in this sheet for convenience. Read-out […]
4th order systems: Interpretation
Introduction Due to limited stiffness, a 4th order system or in other words mechanical systems are characterized by internal resonances which limit dynamical performance, both open-loop and closed-loop. To study the impact of this behavior, a simplified model known as the 4th-order system or 2-mass-spring-damper system is often used. This lumped model is often a […]
Dynamic model in state space
Introduction This sheet is to do a quick scan to the resonances of a desired transfer of a dynamic system via state space approach. From state space a bode-diagram can be created with appropriate software. Equations of Motion (n-dimensional) $underline{M} underline{ddot{x}}+underline{D} underline{dot{x}}+underline{K} underline{x}+underline{F}=underline{0}$ with $underline{x}=left[begin{matrix}x_1&ldots&x_n\end{matrix}right]^Trightarrow n x 1$ $underline{M}=left[begin{matrix}m_1&0&0&0\0&m_2&0&0\0&0&ddots&0\0&0&0&m_n\end{matrix}right]rightarrow n x n$ $underline{K}=left[begin{matrix}K_{11}&K_{12}&ldots&K_{1n}\K_{21}&K_{22}&ldots&K_{2n}\vdots&vdots&ddots&vdots\K_{n1}&K_{n2}&ldots&K_{nn}\end{matrix}right]rightarrow n x n$ […]
Bode plot: Composition and interpretation
Introduction This sheet provides the steps to compose a bode plot of an arbitrary ordinary differential equation. In the resulting bode plot some insights and interpretations are presented, which are also valid for frequency response functions. Composition of bode Step 1: Derive the (Ordinary) Differential Equation$ldots+ mddot{x}+dleft({dot{x}-dot{x}}_{in}right)+cleft(x-x_{in}right)+ldots=F_e$ Step 2: Laplace transform (using $x=x$, $dot{x}=sx$, $ddot{x}=s^2x$, […]
Interpretation of stiffness and damping
Introduction This sheet gives some insight about stiffness and damping and their effect on the dynamics of mechanical systems. Influence of stiffness Stiffness increases the tracking behavior the displacement x of the end-effector (mass m) in relation to the input $x_{in}$ (a stiff actuator). Moreover, it decreases the influence of the external force $F_e$, which […]
3 Parallel & tangential folded leaf springs
Introduction 3 parallel & tangential folded leaf springs are often used as a z, Rx, Ry fixation. Each leaf spring contributes to the total stiffness of the setup. This sheet describes the stiffness and stroke of the individual and the combination of 3 parallel & tangential folded leaf springs @ 120º. Individual stiffness The stiffness […]
Leaf spring/flexure: Reinforced
Introduction Flexures or leaf springs can be used for play and friction free motion. A downside is stiffness and to minimize the needed force, the flexures are made slender and thin. Smart reinforcement of flexures and leaf springs can help to keep the needed motion-force minimal while the flexure or leaf spring is made thicker, […]
Reinforced strut
Introduction Struts are often used for connecting two bodies in 1 DOF (x), while keeping the other DOFs free. In many cases the function of a stiff element with two hinges is desired. This is achieved by reinforcing the midsection of the strut. The poles of the hinges are located at the center of the […]