Harmonic drive

Harmonic drive animation

A Harmonic Drive is a trade mark of the product produced by Harmonic Drive LLC. The basic principle used is a "Strain Wave Gearing" mechanism. It is an input/output gearing mechanism. Claimed characteristics include: no backlash, compactness and light weight, high gear ratio, ratio reconfigurable within a standard housing, good resolution and repeatability when repositioning inertial loads, high torque capability, and coaxial input and output shafts. High gear reduction ratios are possible in a small volume (a ratio of 100:1 is possible in the same space in which planetary gears typically only produce a 10:1 ratio).

Disadvantages include a tendency for 'wind-up', ie a torsional spring rate.

They are typically used in motion control and for gearing reduction, but may also be used to increase rotational speed, or for differential gearing.

History

The basic concept of a Strain Wave gearing was introduced by C.W. Musser in 1957. It was first used successfully in 1964 by Hasegawa Gear Works, Ltd. and USM Co., Ltd. Later, Hasegawa Gear Works, Ltd. became Harmonic Drive Systems Inc. located in Japan and USM Co., Ltd. Harmonic Drive division became Harmonic Drive Technologies Inc.

On January 1, 2006, Harmonic Drive Technologies/Nabtesco of Peabody, MA and HD Systems of Hauppauge, NY, merged to form a new joint venture, Harmonic Drive LLC. HD Systems, Inc. was a subsidiary company of Harmonic Drive System, Inc. Offices are maintained in both Peabody and Hauppauge.

Mechanics

Cross-section of a Strain Wave Gearing.
A: circular spline (fixed)
B: flex spline (attached to output shaft, not shown)
C: wave generator (attached to input shaft, not shown)

The Strain Wave Gearing theory is based on elastic dynamics and utilizes the flexibility of metal. The mechanism has three basic components: a wave generator, a flex spline, and a circular spline. More complex versions have a fourth component normally used to shorten the overall length or to increase the gear reduction within a smaller diameter, but still follow the same basic principles.

The wave generator is made up of two separate parts: an elliptical disk called a wave generator plug and an outer ball bearing. The gear plug is inserted into the bearing, giving the bearing an elliptical shape as well.

The flex spline is like a shallow cup. The sides of the spline are very thin, but the bottom is thick and rigid. This results in significant flexibility of the walls at the open end due to the thin wall, but in the closed side being quite rigid and able to be tightly secured (to a shaft, for example). Teeth are positioned radially around the outside of the flex spline. The flex spline fits tightly over the wave generator, so that when the wave generator plug is rotated, the flex spline deforms to the shape of a rotating ellipse but does not rotate with the wave generator.

The circular spline is a rigid circular ring with teeth on the inside. The flex spline and wave generator are placed inside the circular spline, meshing the teeth of the flex spline and the circular spline. Because the flex spline has an elliptical shape, its teeth only actually mesh with the teeth of the circular spline in two regions on opposite sides of the flex spline, along the major axis of the ellipse.

Assume that the wave generator is the input rotation. As the wave generator plug rotates, the flex spline teeth which are meshed with those of the circular spline change. The major axis of the flex spline actually rotates with wave generator, so the points where the teeth mesh revolve around the center point at the same rate as the wave generator. The key to the design of the harmonic drive is that there are fewer teeth (for example two fewer) on the flex spline than there are on the circular spline. This means that for every full rotation of the wave generator, the flex spline would be required to rotate a slight amount (two teeth, for example) backward relative to the circular spline. Thus the rotation action of the wave generator results in a much slower rotation of the flex spline in the opposite direction.

For a Strain Wave Gearing mechanism, the gearing reduction ratio can be calculated from the number of teeth on each gear:

$reduction\ ratio={\frac {flex\ spline\ teeth-circular\ spline\ teeth}{flex\ spline\ teeth}}$

For example, if there are 202 teeth on the circular spline and 200 on the flex spline, the reduction ratio is: (200 - 202)/200 = -0.01

Thus the flex spline spins at 1/100 the speed of the wave generator plug and in the opposite direction. This allows different reduction ratios to be set without changing the mechanism's shape, increasing its weight, or adding stages. The range of possible gear ratios is limited by teeth size limits for a given configuration.

Holographic Holographic Metamorphic Math Math a hyper plane defined by creating a nth dimensional spheroid with Radients instead of radiens. The Origin of the system is defined as Radients(radiens) = Pi, and the point of origin as z=((tan(x²) + tan(y²)) ²

The statement of claim of the new system is Pythagorean's Therom applied to a hyper plane. Ie the maping of x,y,z,t onto a three dimension space with the point of origin of z=((tan(x²) + tan(y²)) ²

Since the graph itself is holographic, the use of colors for the equations are necessary. Yellow as a base color for time where time is equal to y=e^tan(1)

Example:

 Pointcare conjecture solved by using virtual circles in a manifold space.  When mapped with new system, i -i 0 1 can be used in conjunction to simplify math.  Karnaugh map (K-map for short)

redefining the natural number line to -1,-pi,Delta,pi,1,2 where delta functions as a diferential between movement on the B axis and Pi

Note: Only viewable in 3D will not appear in standard 2d euclidean space.

External links

• Robotic Hand displays Speed of Harmonic Drives
• Kinematic Models for Design Digital Library (KMODDL)
  Movies and photos of hundreds of working mechanical-systems models at Cornell University. Also includes an e-book library of classic texts on mechanical design and engineering.
• Waltmusser.org
• Harmonicdrive.net