Theoretical three-and four-axis gimbal robot wrists

In high-performance flight simulations, a four-axis gimbal system allows all possible rotations with acceptable gimbal angle rates while it avoids the so-callled 'gimbal lock' that occurs when gimbal rotational axes are colinear. In this paper, pertinent equations (including quaternions) are assembled for a hypothetical robot wrist, functionally equivalent to this four-axis gimbal system, and also for a true three-axis gimbal robot wrist. These equations are used to simulate the rotation of a robot hand by the robot wrist in response to operator rotational velocity commands to the robot hand. Near gimbal lock (wrist singularity), excessive rotational rates occur. Scaling the rates, which is necessary for the three-gimbal robot wrist to prevent rate limiting, introduces an undesirable time delay in the robot hand rotation with respect to the commanded rotation. However, the merit of the four-gimbal robot wrist is that the fourth gimbal angle keeps the robot wrist away from the singularity so that the robot hand moves exactly as commanded. It appears that in a 'worst-type' maneuver of the robot hand, the fourth gimbal angle can be defined so that none of the gimbal angle rates exceed about twice the commanded rates

Kinematic rate control of simulated robot hand at or near wrist singularity

A robot hand should obey movement commands from an operator on a computer program as closely as possible. However, when two of the three rotational axes of the robot wrist are colinear, the wrist loses a degree of freedom, and the usual resolved rate equations (used to move the hand in response to an operator's inputs) are indeterminant. Furthermore, rate limiting occurs in close vicinity to this singularity. An analysis shows that rate limiting occurs not only in the vicinity of this singularity but also substantially away from it, even when the operator commands rotational rates of the robot hand that are only a small percentage of the operational joint rate limits. Therefore, joint angle rates are scaled when they exceed operational limits in a real time simulation of a robot arm. Simulation results show that a small dead band avoids the wrist singularity in the resolved rate equations but can introduce a high frequency oscillation close to the singularity. However, when a coordinated wrist movement is used in conjunction with the resolved rate equations, the high frequency oscillation disappears

Superconducting coplanar waveguide resonators for low temperature pulsed electron spin resonance spectroscopy

We discuss the design and implementation of thin film superconducting coplanar waveguide micro- resonators for pulsed ESR experiments. The performance of the resonators with P doped Si epilayer samples is compared to waveguide resonators under equivalent conditions. The high achievable filling factor even for small sized samples and the relatively high Q-factor result in a sensitivity that is superior to that of conventional waveguide resonators, in particular to spins close to the sample surface. The peak microwave power is on the order of a few microwatts, which is compatible with measurements at ultra low temperatures. We also discuss the effect of the nonuniform microwave magnetic field on the Hahn echo power dependence

Ionization Structure and the Reverse Shock in E0102-72

The young oxygen-rich supernova remnant E0102-72 in the Small Magellanic Cloud has been observed with the High Energy Transmission Grating Spectrometer of Chandra. The high resolution X-ray spectrum reveals images of the remnant in the light of individual emission lines of oxygen, neon, magnesium and silicon. The peak emission region for hydrogen-like ions lies at larger radial distance from the SNR center than the corresponding helium-like ions, suggesting passage of the ejecta through the "reverse shock". We examine models which test this interpretation, and we discuss the implications.Comment: 4 pages, 6 figures; To appear in "Young Supernova Remnants" (11th Annual Astrophysics Conference in Maryland), S. S. Holt & U. Hwang (eds), AIP, New York (2001

Translational control of a graphically simulated robot arm by kinematic rate equations that overcome elbow joint singularity

An operator commands a robot hand to move in a certain direction relative to its own axis system by specifying a velocity in that direction. This velocity command is then resolved into individual joint rotational velocities in the robot arm to effect the motion. However, the usual resolved-rate equations become singular when the robot arm is straightened. To overcome this elbow joint singularity, equations were developed which allow continued translational control of the robot hand even though the robot arm is (or is nearly) fully extended. A feature of the equations near full arm extension is that an operator simply extends and retracts the robot arm to reverse the direction of the elbow bend (difficult maneuver for the usual resolved-rate equations). Results show successful movement of a graphically simulated robot arm

Spectral Line Imaging Observations of 1E0102.2-7219

E0102-72 is the second brightest X-ray source in the Small Magellanic Cloud and the brightest supernova remnant in the SMC. We observed this SNR for ~140 ksec with the High Energy Transmission Gratings (HETG) aboard the Chandra X-ray Observatory. The small angular size and high surface brightness make this an excellent target for HETG and we resolve the remnant into individual lines. We observe fluxes from several lines which include O VIII Ly$\alpha$, Ly$\beta$, and O VII along with several lines from Ne X, Ne IX and Mg XII. These line ratios provide powerful constraints on the electron temperature and the ionization age of the remnant.Comment: To appear in "Young Supernova Remnants" (11th Annual Astrophysics Conference in Maryland), S. S. Holt & U. Hwang (eds), AIP, New York (2001

Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN 1006

A joint spectral analysis of some Chandra ACIS X-ray data and Molonglo Observatory Synthesis Telescope radio data was performed for 13 small regions along the bright northeastern rim of the supernova remnant SN 1006. These data were fitted with a synchrotron radiation model. The nonthermal electron spectrum used to compute the photon emission spectra is the traditional exponentially cut off power law, with one notable difference: The power-law index is not a constant. It is a linear function of the logarithm of the momentum. This functional form enables us to show, for the first time, that the synchrotron spectrum of SN 1006 seems to flatten with increasing energy. The effective power-law index of the electron spectrum is 2.2 at 1 GeV (i.e., radio synchrotron-emitting momenta) and 2.0 at about 10 TeV (i.e., X-ray synchrotron-emitting momenta). This amount of change in the index is qualitatively consistent with theoretical models of the amount of curvature in the proton spectrum of the remnant. The evidence of spectral curvature implies that cosmic rays are dynamically important instead of being "test" particles. The spectral analysis also provides a means of determining the critical frequency of the synchrotron spectrum associated with the highest-energy electrons. The critical frequency seems to vary along the northeastern rim, with a maximum value of 1.1e17 (0.6e17 - 2.1e17) Hz. This value implies that the electron diffusion coefficient can be no larger than a factor of ~4.5-21 times the Bohm diffusion coefficient if the velocity of the forward shock is in the range 2300-5000 km/s. Since the coefficient is close to the Bohm limit, electrons are accelerated nearly as fast as possible in the regions where the critical frequency is about 1.0e17 Hz.Comment: 41 pages, 8 figures, accepted by Ap