Conics and a generalised conical pendulum

2019 ◽  
Vol 103 (556) ◽  
pp. 28-40
Author(s):  
Daniel Daners ◽  
Theresa Wigmore
Keyword(s):  
Angular Velocity ◽  
Horizontal Plane ◽  
Circular Motion ◽  
The Other

There is a long tradition of using geometry to solve problems from mechanics. Unfortunately this tradition is not practised much in schools and university any more.With this exposition we would like to demonstrate how elementary properties of ellipses can be used to solve a problem related to the conical pendulum. The problem of the conical pendulum is to consider a mass attached to one end of a light inextensible string of length with the other end attached at the top of a vertical rod. The mass is moving about the rod in uniform circular motion in a horizontal plane. Given the angular velocity of the mass, the question is to determine the angle the string makes with the rod.

Some Dimensions of the Angular Acceleration Receptor Systems of Cephalopods

1984 ◽  
Vol 64 (1) ◽  
pp. 55-79 ◽  
Author(s):  
Linda Maddock ◽  
J. Z. Young
Keyword(s):  
Angular Velocity ◽  
Frequency Band ◽  
Deep Sea ◽  
Horizontal Plane ◽  
Angular Acceleration ◽  
The Body ◽  
The Other ◽  
Radius Of Curvature ◽  
Internal Radius ◽  
Neutrally Buoyant

The shapes and dimensions of the statocysts of cephalopods have been measured and compared with the semi-circular canals of vertebrates. The cavities grow much more slowly than the body as a whole, but there are knobs, anticristae, which restrict the cavity, and these grow relatively faster. This ensures that the flow of endolymph across the cupulae remains small. Where the liquid is constrained within canals the radius of curvature of the whole canal, R, is similar to that of fishes, whereas its internal radius, r, is twice as large in non-buoyant and four times as large in deep-sea buoyant cephalopods as in fishes of similar size. As in fishes the restriction is greatest in the horizontal plane, providing for operation at higher frequencies in turning about the yaw axis.The statocysts of seven species of Loligo all have similar proportions. The largest individuals of 16 genera of non-buoyant squids also have these same relative dimensions. The statocyst of Sepia is more like that of non-buoyant than of other buoyant cephalopods but yet differs significantly from that of Loligo at all sizes. On the other hand 21 genera of squids known to be neutrally buoyant are very different. Their statocysts are often larger than in the non-buoyant forms and there is less restriction of the cavity by anticristae. The greater flow of endolymph acting across the cupulae presumably provides greater sensitivity at the lower frequencies of turning of these deep-sea animals.The data suggest that the cristae of the cephalopod statocyst may operate in the frequency band where they act as angular accelerometers whereas the vertebrate semi-circular canals operate at higher frequencies as angular velocity meters.

scholarly journals Method for Robot Manipulator Joint Wear Reduction by Finding the Optimal Robot Placement in a Robotic Cell

2021 ◽  
Vol 11 (12) ◽  
pp. 5398
Author(s):  
Tomáš Kot ◽  
Zdenko Bobovský ◽  
Aleš Vysocký ◽  
Václav Krys ◽  
Jakub Šafařík ◽  
...  
Keyword(s):  
Angular Velocity ◽  
Dynamic Simulation ◽  
Robot Manipulator ◽  
The Other ◽  
Robotic Arm ◽  
Robotic Cell ◽  
Wear Reduction ◽  
Fixed End ◽  
Robot Placement ◽  
Collaborative Robot

We describe a method for robotic cell optimization by changing the placement of the robot manipulator within the cell in applications with a fixed end-point trajectory. The goal is to reduce the overall robot joint wear and to prevent uneven joint wear when one or several joints are stressed more than the other joints. Joint wear is approximated by calculating the integral of the mechanical work of each joint during the whole trajectory, which depends on the joint angular velocity and torque. The method relies on using a dynamic simulation for the evaluation of the torques and velocities in robot joints for individual robot positions. Verification of the method was performed using CoppeliaSim and a laboratory robotic cell with the collaborative robot UR3. The results confirmed that, with proper robot base placement, the overall wear of the joints of a robotic arm could be reduced from 22% to 53% depending on the trajectory.

scholarly journals 4. On a Thermomagnetic Thermoscope

1880 ◽  
Vol 10 ◽  
pp. 538-539
Author(s):  
W. Thomson
Keyword(s):  
Magnetic Moment ◽  
Horizontal Plane ◽  
Hardened Steel ◽  
The Other ◽  
Silk Fibre ◽  
Steel Wires ◽  
The One

This thermoscope is founded on the change produced in the magnetic moment of a steel magnet by change of temperature. Several different forms suggest themselves: the one which seems best adapted to give good results is to be made as follows:—(1.) Prepare an approximately astatic system of two thin, hardened steel wires, r b, r′ b′, each 1 cm. long, one of them, r, b, hung by a single silk fibre, and the other hung bifilarly from it, by fibres about 3 cms. long, so attached that the projections of the two, on a horizontal plane, shall be inclined at an angle of about ·01 of a radian (or ·57°) to one another.

Contractile differences between muscle units in the medial rectus and lateral rectus muscles in the cat

1986 ◽  
Vol 56 (1) ◽  
pp. 50-62 ◽  
Author(s):  
M. A. Meredith ◽  
S. J. Goldberg
Keyword(s):  
Horizontal Plane ◽  
Complex Interaction ◽  
Contractile Properties ◽  
The Other ◽  
Lateral Rectus ◽  
Medial Rectus ◽  
Types Of Muscle Fibers ◽  
Horizontal Gaze ◽  
Afferent Inputs ◽  
Central Factors

Conjugate eye movements in the horizontal plane are accomplished by the coactivation of the medial rectus (MR) muscle of one orbit and the lateral rectus (LR) muscle of the other. While control of these excursions has been thought to be effected by identical inputs to these muscles, recent studies have demonstrated that MR motoneurons receive different inputs than LR motoneurons. This raises the question of whether the character of the muscles they control are different. The present study evaluated the contractile properties of MR and LR muscle units in the cat. Based on the mechanical aspects of their contractile properties, only two physiological types of muscle units were identified within the MR and LR muscles: twitch and non-twitch muscle units. Twitch muscle units represented over 90% of the units sampled in each muscle. Significant differences in the rate-related and the tension-related contractile properties were demonstrated between MR and LR twitch muscle units. MR muscle units exhibited significantly faster twitch contractions than did LR units. The rate of stimulation at which MR units exhibited fused tetany was significantly higher than for LR units, although units from both muscles demonstrated similar rates of rise of tension at fusion. The rate of rise of tension was closely correlated to tension production (twitch and tetanus) in each muscle. However, MR muscle units demonstrated significantly weaker maximum tetanic tensions and lower tetanus-to-twitch ratios than LR units. These data indicate that while similar physiological types of muscle fibers are present within the MR and LR, MR muscle units are adapted for faster rate-related properties, whereas LR units are adapted for greater tetanic tensions. These distinctions between MR and LR muscle units, coupled with differences between the afferent inputs to their respective motoneurons, suggest that the preservation of conjugacy during horizontal gaze shifts may require a complex interaction of peripheral and central factors.

Numerical Analysis of Temperature Field in Laser Cladding on Teeth Surfaces of Gear Shaft

2010 ◽  
Vol 29-32 ◽  
pp. 571-576
Author(s):  
Lie Chen ◽  
Pei Lin Xie
Keyword(s):  
Temperature Field ◽  
Laser Beam ◽  
Laser Cladding ◽  
Horizontal Plane ◽  
Laser Energy ◽  
The Other ◽  
Analysis Software ◽  
Element Analysis ◽  
Result Show ◽  
Two Sides

Temperature field of laser cladding on teeth surfaces of gear shaft was numerical simulated with finite element analysis software – ANSYS. The simulation result show that the heat caused by laser beam is concentrated inside the tooth mostly. An effect of preheating in the adjacent tooth is also brought about by injected laser energy. In order to make use of the effect of preheating and avoid the concentration of heat, all of the corresponding flanks of teeth should be cladded first and the other flanks of teeth be cladded secondly in the process of laser cladding. It is also shown that the problems of excessive melted down and collapsing of tooth-tip would be easily resulted in by the heat that concentrated in tooth-tip if the tooth-side and tooth-tip be cladded at the same time. The results of analysis and experiment show that at least two times of scanning should be executed in the process of laser cladding on teeth surfaces. At the first scanning, dimension of laser beam should be reduced properly. And the tooth-tip should not be irradiated directly by laser beam. After the first scanning, the gear should be circumrotated a certain angle. And the included angles between the two sides of tooth-tip and horizontal plane should be approximately equal. Then the second scanning could be prosecuted at the tooth-tip. Experiment results show that continuous and compact cladding coat could be gained by this craft. It is proved that this technological craft is reasonable and effective.

scholarly journals Is It Possible to Determine Whether a Star is Rotating About a Unique Axis?

1993 ◽  
Vol 137 ◽  
pp. 566-568 ◽  
Author(s):  
D.O. Gough ◽  
A.G. Kosovichev
Keyword(s):  
Simple Model ◽  
Angular Velocity ◽  
Rotation Axis ◽  
The Other ◽  
The Sun ◽  
Natural Question ◽  
Rotating Stars ◽  
The Core ◽  
Axis Of Rotation ◽  
Fixed Axis

Rotating stars are normally presumed to rotate about a unique axis. Would it be possible to determine whether or not that presumption is correct? This is a natural question to raise, particularly after the suggestion by T. Bai & P. Sturrock that the core of the sun rotates about an axis that is inclined to the axis of rotation of the envelope.A variation with radius of the direction of the rotation axis would modify the form of rotational splitting of oscillation eigenfrequencies. But so too does a variation with depth and latitude in the magnitude of the angular velocity. One type of variation can mimic the other, and so frequency information alone cannot differentiate between them. What is different, however, is the structure of the eigenfunctions. Therefore, in principle, one might hope to untangle the two phenomena using information about both the frequencies and the amplitudes of the oscillations.We consider a simple model of a star which is divided into two regions, each of which is rotating about a different fixed axis. We enquire whether there are any circumstances under which it might be possible to determine seismologically the separate orientations of the axes.

scholarly journals Kinematic Pattern of the Drag-Flick: a Case Study

2012 ◽  
Vol 35 (1) ◽  
pp. 27-33 ◽  
Author(s):  
María Gómez ◽  
Cristina López De Subijana ◽  
Raquel Antonio ◽  
Enrique Navarro
Keyword(s):  
Individual Differences ◽  
Angular Velocity ◽  
Relevant Information ◽  
The Other ◽  
Field Hockey ◽  
Optoelectronic System ◽  
Kinematic Pattern ◽  
The Individual ◽  
Minimum Velocity

The drag-flick is more efficient than hits or pushes when a penalty corner situation is in effect in field hockey. Previous research has studied the biomechanical pattern of the drag-flick, trying to find the cues for an optimal performance. On the other hand, some other studies have examined the most effective visual pick-up of relevant information in shots and goalkeeper anticipation. The aim of this study was to analyse the individual differences in the drag-flick pattern in order to provide relevant information for goalkeepers. One female skilled drag-flicker participated in the study. A VICON optoelectronic system (Oxford Metrics, Oxford, UK) was used to capture the drag-flicks with six cameras. The results showed that the main significant differences between right and left shots (p<0.05) in the stick angles, stick minimum angular velocity and front foot-ball distance were when the front foot heel contacted the floor (T1) and at the minimum velocity of the stick, before the dragging action (T3). The findings showed that the most relevant information might be picked up at the ball-and-stick location before the dragging action.

Two Egyptian Construction Tools

1993 ◽  
Vol 86 (2) ◽  
pp. 166-167
Author(s):  
John F. Lamb
Keyword(s):  
Horizontal Plane ◽  
Vertical Plane ◽  
The Other

Among the objects in the Ramses II exhibition at Fair Park in Dallas in 1989 were two tools from the tomb of Sen-nedjem, one of Ramses II's workmen. One was a level for determining the horizontal plane, the other was a plumb level for determining the vertical plane.

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