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System-Level Modeling of N/MEMS
Published in Sarhan M. Musa, ®, 2018
If a torque that is applied to a nonlinear torsional spring k(θ) = k1 + k2θ2 is related to displacement angle by ΓCL = k(θ)θ, then the torque that the torsional spring applies to the system is Γ = −ΓCL = −k1θ + k2θ3.
Vane Shear Test for Cohesive Soils
Published in Bashir Ahmed Mir, Manual of Geotechnical Laboratory Soil Testing, 2021
Shear strength of sensitive or soft clay deposits is difficult to obtain accurately in the laboratory by conventional “UCS” or triaxial tests as getting undisturbed samples is very difficult because of sampling disturbance. Therefore, the vane shear test is an alternative test in which undrained shear strength of too sensitive or soft clays can be determined. This test is suitable for characterization of saturated clays of soft to medium consistency, highly sensitive or very soft clays without the sample being disturbed by sample preparation or soils which are fissured or highly susceptible to sampling disturbance. The schematic diagram of the VST apparatus is shown in Figure 13.1a. The laboratory vane shear is 10 mm in diameter, 10 mm in height, and 1 mm thick, while the field vanes have diameters ranging from 50 mm to 150 mm. In the laboratory vane shear test, a properly trimmed and undisturbed soft clayey soil sample is placed in a cup and the shear vane is inserted into the specimen up to the desired depth and rotated in the sample by applying torque. It may be noted that the torque is gradually applied to the upper end of the torque rod until the soil fails in shear due to the rotation of the vanes. It is assumed that the undrained shear strength (cu) is constant throughout the sheared soil sample. The applied torque is measured by a torsion spring of specified stiffness by recording the angle of twist (θ). When soil is stressed to its shear strength, the vanes will rotate (@ 0.1o/sec or 1° per minute or with a rate of 1 revolution per second) in the soil. The resistance to applied torque in the soil sample is mobilized throughout the vertical and horizontal faces of the soil sample of diameter “D” and the diameter of vane. Since the soil fails along a cylindrical surface, the shearing resistance can be calculated from the vane dimensions and the applied torque. It may be noted that the undrained strength varies as zero at the center and maximum value at the outer surface (e.g. R = D/2), as shown in Figure 13.1. Also, there could various types of variation of mobilization of shear strength from the center of the torque to the outer end as shown in Figure 13.1(b). Assuming that distribution of shear resistance is linearly increasing with increasing radius of the soil sample, then the shear stress can be expressed as: τ=[cu2RD](R→0atcentreR→D/2atoutersurface)
Control of swarm behavior for a batteryless and sensorless small jumping robot using wireless power supply
Published in Advanced Robotics, 2023
Tomoki Miyashita, Takashi Takuma
The jumping mechanism is based on that of an ant, called Odontomachus monticola [12], which leaps by quickly closing its large jaws. LABIC3 leaps by instantaneously closing its legs and pushing the foot. The configuration of the gearbox is shown in Figure 1(b,c). The motor drives gear I with 16 teeth. Gear II, with 32 teeth, couples on a segmented gear with four teeth and some missing sections, as shown in Figure 1(d). Legged gears I and II with 32 teeth (partial legs), which connect the legs, roll the torsion with their rotation. The legs are interlocked with the slider attached to the foot via a Scotch yoke mechanism, and a force is applied to the foot. A torsion spring was selected to provide a sufficient torque for jumping. The motor was selected to be commercially available and capable of applying sufficient force to a torsion spring. The gear ratio was determined such that the time required to jump and a sufficient force can be applied to the torsion spring. The length of the legs, shown in Figure 3, was chosen in consideration of the balance between the force required for the small size and jumping to ensure that a sufficient force is applied to the legs.
Precision control of miniature SCARA robots for multi-object spectrographs
Published in International Journal of Optomechatronics, 2020
Luzius Kronig, Philipp Hörler, Stefane Caseiro, Loic Grossen, Ricardo Araujo, Jean-Paul Kneib, Mohamed Bouri
Figure 11 shows the measured positive and negative break-away torque for one full turn of the motor. The Figure shows that a higher torque is needed to turn the motor in the negative direction since it has to push against the torsion spring. Furthermore, both curves have a double sinusoid, which reveals a cogging torque Tcog with two favorable positions per motor turn. One full turn of the motor moves the output only slightly due to the reduction, and hence the torque of the spring here is assumed constant. The superposition of torsion spring, Coulomb friction, and cogging torque is apparent. By averaging the break-away torque over the full turn, we can calculate the Coulomb constant and the local torque of the spring:
Gait assist brace with double carbon fiber reinforced plastic spring blades to allow ankle joint movement and change in walking direction
Published in Advanced Robotics, 2021
Iwori Takeda, Wataru Yasunaga, Satoshi Kobayashi, Yusaku Tagawa, Hiroshi Onodera
The bending and restoring process of the L-shaped CFRP spring is similar to that of a helical torsion spring. The maximum plantarflexion angle of the ankle joint during walking is approximately 10° [25,26]. The assist torque of the ankle joint is thus 0.75 Nm/kg when the CFRP bends by 10°Collins et al. demonstrated that using an unpowered gait assist system that delivers an assist torque of 0.4 Nm/kg to the ankle joint can reduce the metabolic cost by approximately 7% [2]. Quinlivan et al. reported that providing an assist torque of 0.5 Nm/kg to the ankle joint can reduce the metabolic rate of walking by approximately 23% [27].