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There is no radial clearance because two arms of the stepped wheel are always in contact with the double cam. Generally, combined contacts may be used to avoid the jerk and wear and noise associated with a single follower such as a single follower gliding along a slot and changing its contact point from one side of the slot to the other can be avoided by using two followers sliding along the same slot, one side each.
An elastically deformable mass deforms under an applied force or acceleration ; the deformation is a function of its stiffness and the magnitude of the force.
If the change in force is slow, the jerk is small, and the propagation of deformation is considered instantaneous as compared to the change in acceleration.
The distorted body acts as if it were in a quasistatic regime , and only a changing force nonzero jerk can cause propagation of mechanical waves or electromagnetic waves for a charged particle ; therefore, for nonzero to high jerk, a shock wave and its propagation through the body should be considered.
The propagation of deformation is shown in the graphic "Compression wave patterns" as a compressional plane wave through an elastically deformable material.
Also shown, for angular jerk, are the deformation waves propagating in a circular pattern, which causes shear stress and possibly other modes of vibration.
The reflection of waves along the boundaries cause constructive interference patterns not pictured , producing stresses that may exceed the material's limits.
The deformation waves may cause vibrations, which can lead to noise, wear, and failure, especially in cases of resonance. The graphic captioned "Pole with massive top" shows a block connected to an elastic pole and a massive top.
The pole bends when the block accelerates, and when the acceleration stops, the top will oscillate damped under the regime of pole stiffness.
One could argue that a greater periodic jerk might excite a larger amplitude of oscillation because small oscillations are damped before reinforcement by a shock wave.
One can also argue that a larger jerk might increase the probability of exciting a resonant mode because the larger wave components of the shock wave have higher frequencies and Fourier coefficients.
To reduce the amplitude of excited stress waves and vibrations, one can limit jerk by shaping motion and making the acceleration continuous with slopes as flat as possible.
Due to limitations of abstract models, algorithms for reducing vibrations include higher derivatives, such as jounce , or suggest continuous regimes for both acceleration and jerk.
One concept for limiting jerk is to shape acceleration and deceleration sinusoidally with zero acceleration in between see graphic captioned "Sinusoidal acceleration profile" , making the speed appear sinusoidal with constant maximum speed.
The jerk, however, will remain discontinuous at the points where acceleration enters and leaves the zero phases. Roads and tracks are designed to limit the jerk caused by changes in their curvature.
On railways, designers use 0. Recall that in constant-speed motion along an arc, jerk is zero in the tangential direction and nonzero in the inward normal direction.
Transition curves gradually increase the curvature and, consequently, the centripetal acceleration. An Euler spiral , the theoretically optimum transition curve, linearly increases centripetal acceleration and results in constant jerk see graphic.
In real-world applications, the plane of the track is inclined cant along the curved sections. The incline causes vertical acceleration, which is a design consideration for wear on the track and embankment.
The Wiener Kurve Viennese Curve is a patented curve designed to minimize this wear. Rollercoasters  are also designed with track transitions to limit jerk.
S-shaped curves, such as figure eights, also use track transitions for smooth rides. In motion control , the design focus is on straight, linear motion, with the need to move a system from one steady position to another point-to-point motion.
The design concern from a jerk perspective is vertical jerk; the jerk from tangential acceleration is effectively zero since linear motion is non-rotational.
Motion control applications include passenger elevators and machining tools. Limiting vertical jerk is considered essential for elevator riding convenience.
For hospitals, 0. A primary design goal for motion control is to minimize the transition time without exceeding speed, acceleration, or jerk limits.
Consider a third-order motion-control profile with quadratic ramping and deramping phases in velocity see figure. Segment four's time period constant velocity varies with distance between the two positions.
If this distance is so small that omitting segment four would not suffice, then segments two and six constant acceleration could be equally reduced, and the constant velocity limit would not be reached.
If this modification does not sufficiently reduce the crossed distance, then segments one, three, five, and seven could be shortened by an equal amount, and the constant acceleration limits would not be reached.
Other motion profile strategies are used, such as minimizing the square of jerk for a given transition time  and, as discussed above, sinusoidal-shaped acceleration profiles.
Motion profiles are tailored for specific applications including machines, people movers, chain hoists, automobiles, and robotics.
Jerk is an important consideration in manufacturing processes. Rapid changes in acceleration of a cutting tool can lead to premature tool wear and result in uneven cuts; consequently, modern motion controllers include jerk limitation features.
In mechanical engineering, jerk, in addition to velocity and acceleration, is considered in the development of cam profiles because of tribological implications and the ability of the actuated body to follow the cam profile without chatter.
A device that measures jerk is called a "jerkmeter". Further time derivatives have also been named, as snap or jounce fourth derivative , crackle fifth derivative , and pop sixth derivative.
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