© 2002 by CRC Press LLC of this micro-velocity-sensor was tested in a two-dimensional, flat-plate boundary layer at a Reynolds number based on distance from the leading edge of 4.2 × 10 6 . Figure 16.12 compares the mean velocity profile in a turbulent boundary layer as measured with a conventional and MEMS-based sensor. The microsensor measured mean velocities with the same accuracy as a corresponding conventional hot-wire. Moreover, it was also demonstrated that the microsensor had spatial and temporal resolutions that made it suited for turbulence measurements. Figure 26.13 shows the streamwise turbulence intensity and the Reynolds stress as measured by a conventional X-wire and by two silicon microsensors. The MEMS- based sensors operated with good resolution even when the temperature of the heated part was reduced considerably. A clear drawback of this micro-hot-film is the proximity of the heated part of the sensor to the surface of the chip, rendering the probe insensitive to changes in flow direction. This makes the silicon sensor unsuited for use in three-dimensional flows where the primary flow direction is not known a priori. Jiang et al. (1994) presented a MEMS-based velocity sensor with the hot-wire freestanding in space without any nearby structures, so that cooling velocities can be determined in the same way as with a conventional hot-wire. Their sensor is shown in Figure 26.14 and has a polysilicon hot-element that is greatly reduced in size, typically about 0.5 µm thick, 1 µm wide, and 10–160 µm long. The dynamic performance and sensitivity of this sensor have been tested. A heating time of 2 µs and a cooling time of 8 µs for the 30-µm-long sensor in constant-current mode have been achieved. For constant-temperature operation, a time constant of 0.5 µs for the 10-µm-long sensor has been recorded. The corresponding cut-off frequency is 1.4 MHz. The calibration curves of a 20- µm-long micro-hot-wire at two different angles are shown in Figure 26.15. The average sensitivity was found to be 20 mV/m/s at an input current of 0.5 mA. No turbulence measurements have been reported using this sensor. Noteworthy is that the silicon hot-wires have a trapezoidal cross section, which might cause severe uncontrolled errors in turbulence measurements. A severe drawback of commercially available triple hot-wire probes is the large measuring volume, typically a sphere with a diameter of 3 mm. This is far too large to be acceptable for turbulence measurements at realistic Reynolds numbers. Ebefors et al. (1998) have presented a MEMS-based triple- hot-wire sensor, shown schematically in Figure 26.16. The x- and y-hot-wires are located in the wafer plane while the z-wire is rotated out of the plane using a radial polyimide joint. The silicon chip size is 3.5 × 3.0 × 0.5 mm 3 , and the three wires are each 500 × 5 × 2 µm 3 . The sensor is based on the thermal anemometer principle, and the polyimide microjoint technique is used to create a well-controlled, FIGURE 26.12 Typical mean velocity profile measured with a MEMS sensor and a conventional single hot-wire. Here, U/u τ = f (u τ y/v), where u τ is the friction velocity. (From Löfdahl, L. et al. (1992) Exp. Fluids, 12, 391–393. © 1992 Springer-Verlag. With permission.) U + = U/u τ 0 110 U + = y + 100 1000 Hot-wire Silicon sensor 10 20 30 y + = u τ y/ν U + = ln y + + 5.0 1 0.41 © 2002 by CRC Press LLC of this micro-velocity-sensor was tested in a two-dimensional, flat-plate boundary layer at a Reynolds number based on distance from the leading edge of 4.2 × 10 6 . Figure 16.12 compares the mean velocity profile in a turbulent boundary layer as measured with a conventional and MEMS-based sensor. The microsensor measured mean velocities with the same accuracy as a corresponding conventional hot-wire. Moreover, it was also demonstrated that the microsensor had spatial and temporal resolutions that made it suited for turbulence measurements. Figure 26.13 shows the streamwise turbulence intensity and the Reynolds stress as measured by a conventional X-wire and by two silicon microsensors. The MEMS- based sensors operated with good resolution even when the temperature of the heated part was reduced considerably. A clear drawback of this micro-hot-film is the proximity of the heated part of the sensor to the surface of the chip, rendering the probe insensitive to changes in flow direction. This makes the silicon sensor unsuited for use in three-dimensional flows where the primary flow direction is not known a priori. Jiang et al. (1994) presented a MEMS-based velocity sensor with the hot-wire freestanding in space without any nearby structures, so that cooling velocities can be determined in the same way as with a conventional hot-wire. Their sensor is shown in Figure 26.14 and has a polysilicon hot-element that is greatly reduced in size, typically about 0.5 µm thick, 1 µm wide, and 10–160 µm long. The dynamic performance and sensitivity of this sensor have been tested. A heating time of 2 µs and a cooling time of 8 µs for the 30-µm-long sensor in constant-current mode have been achieved. For constant-temperature operation, a time constant of 0.5 µs for the 10-µm-long sensor has been recorded. The corresponding cut-off frequency is 1.4 MHz. The calibration curves of a 20- µm-long micro-hot-wire at two different angles are shown in Figure 26.15. The average sensitivity was found to be 20 mV/m/s at an input current of 0.5 mA. No turbulence measurements have been reported using this sensor. Noteworthy is that the silicon hot-wires have a trapezoidal cross section, which might cause severe uncontrolled errors in turbulence measurements. A severe drawback of commercially available triple hot-wire probes is the large measuring volume, typically a sphere with a diameter of 3 mm. This is far too large to be acceptable for turbulence measurements at realistic Reynolds numbers. Ebefors et al. (1998) have presented a MEMS-based triple- hot-wire sensor, shown schematically in Figure 26.16. The x- and y-hot-wires are located in the wafer plane while the z-wire is rotated out of the plane using a radial polyimide joint. The silicon chip size is 3.5 × 3.0 × 0.5 mm 3 , and the three wires are each 500 × 5 × 2 µm 3 . The sensor is based on the thermal anemometer principle, and the polyimide microjoint technique is used to create a well-controlled, FIGURE 26.12 Typical mean velocity profile measured with a MEMS sensor and a conventional single hot-wire. Here, U/u τ = f (u τ y/v), where u τ is the friction velocity. (From Löfdahl, L. et al. (1992) Exp. Fluids, 12, 391–393. © 1992 Springer-Verlag. With permission.) U + = U/u τ 0 110 U + = y + 100 1000 Hot-wire Silicon sensor 10 20 30 y + = u τ y/ν U + = ln y + + 5.0 1 0.41 © 2002 by CRC Press LLC 27 Surface-Micromachined Mechanisms 27.1 Introduction 27.2 Material Properties and Geometric Considerations Stress and Strain • Young’s Modulus • Poisson’s Ratio • Contact Stresses • Stress in Films and Stress Gradients • Wear • Stiction 27.3 Machine Design Compliance Elements—Columns, Beams and Flexures • Columns • Beams • Stress Concentration • Cantilever Beam Springs • Fixed Beam Springs • Flexures • Springs in Combinations • Buckling 27.4 Applications Microengine • Countermeshing Gear Discriminator • Micro-Flex Mirror 27.5 Failure Mechanisms in MEMS Vertical Play and Mechanical Interference in Out-of-Plane Structures • Electrical Shorts • Lithographic Variations • Methods of Increasing the Reliability of Mechanisms Acknowledgments 27.1 Introduction Surface-micromachining technologies have offered the following advantages to mechanism users and designers: smaller machines, different physical effects that dominate at the microscale, and reduced assembly costs. The advantages of smaller machines are sometimes very important. For example, small machines are important in aviation and space applications where a decrease in size and weight corre- sponds to an increased range or a reduction in the amount of fuel required for a given mission. The advantages of the different physical effects that dominate at the microscale are less obvious. Mechanisms that operate at high frequencies can greatly benefit (or suffer) from the reduced influence of inertia (typical of surface-micromachined devices) if the aim is to start and stop quickly. Smaller scales also mean surface-micromachined mechanisms are more resistant to shock and vibration than macrosized mechanisms because the component strength decreases as the square of the dimensions while the mass and inertia decrease as the cube of the dimensions. Another difference is that forces, such as van der Waals forces and electrostatic attraction, are much more important at the microscale than at the macro- scale. Reduced assembly costs are another advantage of surface-micromachined mechanisms. Surface micromachining in most cases allows the creation of machines that are assembled at the same time as their constituent components. Instead of using skilled workers to assemble intricate mechanisms by hand or investing in complicated machinery, the assembly is done as a batch process during the integrated- circuit-derived fabrication process. Preassembly does impose certain limitations on the designer, such as the inability to build devices with as-fabricated stored mechanical energy. Instead, structures such as Andrew D. Oliver Sandia National Laboratories David W. Plummer Sandia National Laboratories . Smaller scales also mean surface-micromachined mechanisms are more resistant to shock and vibration than macrosized mechanisms because the component strength decreases as the square of the dimensions. than at the macro- scale. Reduced assembly costs are another advantage of surface-micromachined mechanisms. Surface micromachining in most cases allows the creation of machines that are assembled. polyimide joint. The silicon chip size is 3.5 × 3.0 × 0.5 mm 3 , and the three wires are each 500 × 5 × 2 m 3 . The sensor is based on the thermal anemometer principle, and the polyimide microjoint