Showing papers on "Rotation around a fixed axis published in 1972"

Rotational Relaxation of Molecules in Fluids for Reorientations of Arbitrary Angle

Abstract: A theory of rotational motion of molecules in liquids is presented. The traditional Debye diffusion model is generalized so as to include arbitrary reorientation angles by means of a nonlocal master equation. Random walk models are a special case of this generalization. We have obtained the conditional probabilities for the orientation of a body and of a vector fixed in the body for arbitrary body geometry. These results are then specialized to specific symmetries. From these conditional probabilities we calculate correlation functions which describe a large number of spectroscopic experiments such as NMR, ESR, NQR, dielectric relaxation, and infrared and Raman spectroscopy. We find that the form of these results for the correlation functions depend only on medium isotropy and body geometry. The same number of decaying exponentials are found as in the diffusion model regardless of the details of the reorientation mechanism. Only the amplitudes and relaxation times depend on these details.

Effects of gravity-gradient torque on the rotational motion of a triaxial satellite in a precessing elliptic orbit.

Abstract: A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order inn/ω0, wheren is the orbital mean motion of the center of mass andω0 is a reference value of the magnitude of the satellite's rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed and a comparison of theoretical results with observations is made.

Rotational Diffusion Model with a Variable Collision Distribution

Abstract: Starting with an m‐diffusion model a matrix description is given of the rotational motion of a dipole molecule undergoing frequent collisions. This treatment gives rise to an analytical expression for the dipole correlation function and for the angular momentum correlation function in which a limited number of parameters from the model appear. It is argued that the collision distribution which determines the rotational diffusion process need not necessarily be a Poisson distribution. In liquids with strong interactions the distribution is governed by the frequency distribution of the medium. This leads to the inclusion of a librational motion in the rotational diffusion model. A comparison of simulations with different collision distributions and experimental data is given.

Gear arrangement for providing an oscillating rotational motion

Abstract: A pair of meshed gears each of which comprises a plurality of sectors having the configuration of a logarithmic spiral provide an oscillating motion with respect to each other as they rotate. The gears can be coupled to the rotors of rotary piston machines and the like to provide the desired oscillating rotational motion thereto.

Apparatus for cutting irregular edge contours in relatively flat workpieces

Abstract: A machine is disclosed for edge cutting relatively flat sheet material into pieces having any desired irregular configuration. An overhead radial arm supports a cutting tool in a fixed position in space and a lower work holding support is mounted for movement in a horizontal plane in a direction toward and away from the tool and for rotation about its axis, and holds the work preferably as by a vacuum applied to the underside of the work. By manipulating the work holder in simultaneous rotary motion about its own axis and reciprocatory motion toward and away from the tool, the work is moved relative to the cutting tool so as to cause the tool to cut along any non-symetrical or irregular contour as may be desired as well as symetrical shapes, and as controlled by a preformed template held by the work holder.

The stability of motion of satellites with flexible appendages

Abstract: The mathematical formulation associated with the problem of stability of motion of a satellite consisting of a main rigid body and three (or less) pairs of flexible rods is presented. The rods are capable of flexure in two orthogonal directions. Whereas the rotational motion of the body is described by generalized coordinates depending on time alone, the elastic displacements of the rods depend both on spatial position and time. Assuming no external torques, there exist motion integrals in the form of momentum integrals. These integrals can be regarded as constraint equations relating the system velocities, and used to reduce the number of variables describing the motion. The stability analysis has been carried out by means of an extension of the Liapunov direct method. Since the elastic vibrations result in energy dissipation, it is shown that the equilibrium position is asymptotically stable if the Hamiltonian is positive definite and unstable if it can take negative values in the neighborhood of the equilibrium. Determining the sign definiteness of the Hamiltonian is complicated by the fact that it contains spatial derivatives of the elastic displacements. Two methods are presented to cope with this problem. The first, the standard modal analysis in conjunction with series truncation, develops criteria in terms of infinite series associated with the natural modes and frequencies of the elastic rods. The second, the method of integral coordinates, yields closed-form stability criteria involving the system parameters, such as the body moments of inertia, the length and mass distribution of the rods, the lowest natural frequencies of the rods, and the satellite spin velocity.

Convective instability of a rotating fluid

Abstract: A physical system may be in thermodynamic equilibrium when participating as a whole in uniform rotational motion [1]. In particular, mechanical equilibrium of a liquid in a cavity rotating about a stationary axis with the constant angular velocity Ω (“solid-body” rotation of the liquid) is possible. If the liquid is uniform in composition and isothermal, then such equilibrium, as shown in [2], is stable for all Ω. However, in the case of a nonuniformly heated liquid, stability of the solid-state rotation is, generally speaking, impossible.

Rotary type energy absorber with axial drive and automatic resetting capability

Abstract: A rotary type energy absorber combined with means for converting a linearly acting force into a torque for driving a rotary element of the energy absorber, the linearly acting force being aligned with the axis of the energy absorber. Forces acting on the energy absorber are aligned with its axis, and there are no bending movements introduced. The linearly acting force is converted to a rotary motion by gear means in the form of telescoping threaded members. A spring is provided normally acting upon the device to reset it into an initial position after an impacting force has been received, a clutch being provided to allow free rotation of the energy absorber when being reset.

Electromagnetic drive system

Abstract: A machine for generating compressive energy from kinetic energy, comprising a plurality of weights mounted for rotation on a shaft which is disposed at an angle with respect to the axis of rotation. The shaft, and the weights mounted thereon, are driven about the axis of rotation by an electromagnetic drive comprising a segmented annular electromagnet, each segment of which is energized in advance of a magnetically sensitive element on the shaft to rotate the element, shaft and the weights about the axis. By suitable crankshaft linkage, the rotational motion is transmitted to linear motion of pistons which yield the compressive energy to be generated.

Power transmission mechanism

Abstract: A power transmission mechanism having a reciprocating drive means for imparting rotation to a reversibly rotatable body is improved by having an output drive member connected to the rotatable body and resilient means connecting the rotatable body and the output drive member for transmitting the rotational motion of the rotatable body to the output drive member. The resilient means is deflectable so that it can deflect from its normal position to store a portion of the rotational energy while transmitting the remainder of the rotational energy in the form of rotational movement to the output drive member while the reversibly rotatable body is rotating. The resilient means then reverts to its normal position to release the stored energy and continue moving the output drive member after the reversibly rotatable body is stopped.

Precision linear motion converting and position measuring apparatus

Abstract: A roller-band device including an idler roller, drive roller and band, is mounted on a carriage movable linearly relative to the band so that the angle of rotation of the drive roller is related to the distance traveled by the carriage. The drive roller can be driven to convert rotary motion to linear motion or the carriage can be driven to convert linear motion to rotary motion. Means including a pulse generator coupled to the drive roller produces a very accurate readout of the position of the carriage.

Device for imparting an alternating rotary motion to a body, about a mechanical axis

Abstract: To a body, imparted in alternating rotary motion about a mechanical axis attached to a fixed support, by a motor, there are fixed the ends of springs whose respective other ends are connected to said fixed support. The springs restore, in the form of kinetic energy, the stored potential energy; the energy to be supplied by the motor in order to sustain the motion, is limited to that required to compensate for friction losses. An angle detector supplies a control signal from a negative feedback loop in the motor supply, the motor supply also comprising an ordinary feedback or reaction loop.

Steady flow of a polar fluid in a rotating pipe

Abstract: It is shown that the axial motion and rotational motion in the steady flow of a polar fluid in a rotating cylinder are coupled, and that the rotational motion is not a rigid body rotation. For the same problem in traditional viscous fluid theory the axial motion and rotational motion are uncoupled, and the rotational motion is a rigid body rotation.

A Linearized Chain Model for Dielectric Loss in Polymers

Abstract: In order to treat dielectric dispersion arising from the motions of main-chain dipoles perpendicular to the polymer chain axis, the polymer molecule is approximated by a linear mechanical model consisting of a chain of torsional springs, dashpots, and beads bearing dipoles. The equations of rotational motion can be solved analytically for this model. We derive an expression for the correlation length, a measure of the extent to which rotational motion is correlated along the chain. We obtain equations for the dielectric dispersion.

Device for converting reciprocating motion to rotary motion

Abstract: 1,260,112. Cams. O. W. SMITH, and P. M. BARTLE. 3 Feb., 1969 [3 Nov., 1967], No. 50109/67. Heading F2K. [Also in Division F1] A device for converting reciprocating motion to rotary motion comprises a first part 1 which includes a cam surface and a second part 2 which parts are mounted for relative rotation about an axis and one or more pairs of members 5, 6 mounted on the second part for relative reciprocation in a plane transverse to the axis. In operation, one member of each pair is 180 degrees out of phase with the other member in the pair and at least one of the members reacts indirectly by means of a lever 7, 8 pivoted on the second part and means connects each of the members to a cam follower 9, 10 against the cam surface, thereby causing a relative rotation of the first and second part. In a modification (not shown), the members act through cranked levers and rollers on a fixed internal cam.

Oscillatory output devices

Abstract: A device for converting continuous rotary motion to oscillatory motion comprising an annular continuously rotatable member rotatable about a first fixed axis, an eccentric member mounted within the continuously rotatable member for rotation about a second movable axis parallel but eccentric to the first axis, and an output member rotatable about a third fixed axis parallel to the first and second axes, the eccentric and output members being interconnected for relative rotational movement about a fourth movable axis parallel to the third axis, the inter-relation of the four axes being such that continuous rotation of the continuously rotatable member produces displacement of the second axis about the first axis, resulting in oscillatory movement of the eccentric within the continuously rotatable member, which in turn produces oscillatory movement of the output member by virtue of the oscillation of the fourth axis about the third axis.

Zur Relaxation eines Kernspinpaares bei behinderter Bewegung

Abstract: Redfield's density matrix theory has been applied to a pair of equal spins rotating around a fixed axis. The results of Bloembergen's wellknown paper [1] were corrected. For calculating the spectral densities of the stochastic rotational motion the theory of Ivanov and Valjev [2] has been used which holds for large rotational jumps between equal potential wells. The formulae are compared with the results of Look and Lowe [3] for the hindered molecular rotation between unequal potential wells.

Differential-motion timer

Abstract: A differential-motion timer. Reciprocating motion of a predetermined frequency and angular displacement is converted into unidirectional rotary motion by means of at least two ratchet wheels coaxially aligned and independently free-wheeling and each having a different number of notches. Each of the ratchet wheels is driven by a ratchet drive which is connected to the reciprocating element. Accordingly, each ratchet wheel can convert reciprocating motion to unidirectional rotary motion, the speed of the rotary motion being, on the average, proportional to the driver frequency. Since each of the ratchet wheels has a different number of notches, it follows that each of the wheels will be driven at a slightly different speed by the single ratchet driver. This difference speed is the timing motion and the relative angular positions of the wheels correspond to the elapsed time. A switch is actuated whenever certain preselected corresponding points on each of the ratchet wheels arrive at predetermined positions.