Position, Velocity, & Acceleration

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1 Position, Velocity, & Acceleration San José State University A. Mysore Spring 2009

2 Position, Velocity, and Acceleration v t} = ds dt { { t} = s + o s v{ t} dt t t o a t} = dv dt { { t} = v + o v a{ t} dt t t o San José State University A. Mysore Spring

3 Sensing Principles vs. Measurement Devices Sensing Principles Electrical resistance Electrical capacitance Electromagnetism Photoelectric effect Piezoelectric effect Hall effect Doppler effect Interferometry etc. Measurement Devices Potentiometers LVDT Optical Encoders Tachometers Accelerometers Interferometers Triangulation Sensors Capacitance Sensors etc San José State University A. Mysore Spring

4 Potentiometers Potentiometer is a variable voltage divider V = x L o V s Angular Potentiometers are used in the volume/tone control of Radio, TV etc. San José State University A. Mysore Spring

5 Linear Variable Differential Transformer (LVDT) Smaller Displacement Measurements Linear only over a certain range Coil made of Ferromagnetic material San José State University A. Mysore Spring

6 LVDT Signal Output Phase relation of the output signal with respect to the primary indicates the direction San José State University A. Mysore Spring

7 Capacitive Displacement Sensing C = ε o εr A d C: capacitance ε: permittivity A: plate area d: distance between plates San José State University A. Mysore Spring

8 Capacitance Sensor Images from Lion Precision Company Web Site San José State University A. Mysore Spring 2009

9 Position Encoders May be arranged in linear or rotary configuration. Optical detection is common, but may also be capacitive, resistive, magnetic, etc. May be absolute or incremental (counting from a reference). Arranging in quadrature provides finer resolution (by monitoring transitions rather than states) as well as direction. San José State University A. Mysore Spring

10 Photoelectric Effect e - n-type Silicon (e.g. Phosphorous-doped) with electrons in excess p-n junction acts as barrier h + p-type Silicon (e.g. Boron-doped) with electrons in shortage The photoelectric effect is a phenomenon in which photon energy (i.e. from light) releases electrons from their otherwise more stable state on a surface. In a photodiode, photon energy produces free charge carriers (electron-hole pairs) to overcome the otherwise current-impeding junction between p-doped and n- doped semiconductor layers. San José State University A. Mysore Spring

11 Laser Interferometer Fixed Reflector Moving Reflector Source Mirror Analyzer San José State University A. Mysore Spring

12 Hall Effect The Hall effect is a disruption to the ordinary flow of current and charge distribution across a thin sheet (typically semiconductor) by the presence of a magnetic field oriented perpendicular to it. The electrons traveling across the sheet are displaced by the magnetic component (B) of the Lorentz force: r r r r F = q( E + v B) A wide variety of Hall effect sensors can thus measure magnetic field strength or subtle changes in field by outputting a voltage that is proportional to it. January 2007 San José State University A. Mysore Spring

13 Tachometer A tachometer is a device that measures angular velocity. Some implementations may include electromagnetic generators, magnetic pickups, and photo-detectors. San José State University A. Mysore Spring

14 Accelerometer Senses acceleration (i.e. changes in velocity) by measuring position as a function of time. A mechanical vibration system having springmass-damper elements. Commonly expressed in multiples or fractions of g (9.81 m/s²). Image(s) from: San José State University A. Mysore Spring

15 Piezoelectric Effect Piezoelectricity is a two-way relationship between mechanical stress and electric potential exhibited by some materials, based on changes in the crystalline ionic structure along internal asymmetries. Based on related phenomena, piezoresistive materials exhibit change in electrical resistance when experiencing mechanical strain. MEMS & Microsystems: Design and Manufacture by T. R. Hsu, McGraw-Hill, 2002 San José State University A. Mysore Spring

16 MEMS Accelerometers (Analog Devices ADXL) Features 2-Axis Acceleration Sensor ~ 5mm x 5 mm chip g operating ranges milli-g resolution ma power consumption ~ 1000 g Shock Survival Applications Inertial Navigation Portable Device Security Motion Detection Camera Image Stabilization Game Controller Feedback Images from San José State University A. Mysore Spring

17 Some Useful Criteria for Position/Motion Sensors Contact vs. Non-Contact Range Resolution Accuracy Repeatability Frequency Response Signal Conditioning Requirements Environmental Robustness Cost San José State University A. Mysore Spring

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