Harmonic Drives

The rotational motion comes from an input shaft that can be a servo motor axis for example. This is connected to an element called “wave generation” which has an elliptical shape and is encircled by an elliptical ball bearing. As the shaft rotates, the edges change position, so it looks like it is generating a motion wave. This part is inserted inside a flex spline that is made out of a torsionally stiff yet flexible material.

The material takes up this wavy motion by flexing according to the rotation of the input shaft and also creates an elliptical shape. The outer edge of this flex spline features gear teeth that are suitable for transferring high loads without any problem. To transfer these loads, the flex spline is fitted inside the circular spline which is a round gear featuring internal teeth.

This outer ring is rigid and its internal diameter is marginally larger than the major axis of the ellipse formed by the flex spline. This means that the circular spline does not assume the elliptical shape of the other two components, but instead, it simply meshes its inner teeth with those of the outer flex spline side, resulting in the rotation of the flex spline.

The rate of rotation is dependent on the rotation of the input shaft and the difference in the number of teeth between the flex spline and the circular spline. The flex spline has fewer teeth than the circular spline, so it can rotate at a much reduced ratio and in the opposite direction than that of the input shaft. The reduction ration is given by: (number of flex spline teeth – number of circular spline teeth) / number of flex spline teeth.

So for example, if the flex spline has 100 teeth and the circular spline has 105, the reduction ratio is (100 - 105) / 100 = -0.05 which means that the flex spline ration is -5/100 (minus indicates the opposite direction of spin). The difference in the number of teeth can be changed to accommodate different reduction ratios and thus different specialized needs and requirements.

There are three elements in a basic Harmonic Drive: a circular spline, a flexspline, and a wave generator. The circular spline has internal teeth that mesh with external teeth on the flexspline. The flexspline has fewer teeth and consequently a smaller effective diameter than the circular spline.

The wave generator is elliptical in shape and acts as a link with two rollers that rotates within the flexspline, causing it to mesh with the circular spline progressively at diametrically opposite points. If the wave generator (the input) rotates clockwise while the circular spline is fixed, the flexspline (the output) will rotate or roll inside the circular spline at a much slower rate in a counterclockwise direction.

The ratio of the input speed to the output speed depends on the difference in the number of teeth in the circular spline and on the flexspline. Speed ratios as high as 320 to 1 can be produced in single-reduction Harmonic Drives, which are lighter, smaller, and more efficient than conventional high-ratio drives. Compound drives can produce ratios as high as 1,000,000 to 1. Either the circular spline, the flexspline, or the wave generator may be fixed while the other two elements serve as input and output.

A unique and useful characteristic of the Harmonic Drive is its ability to transmit motion through sealed walls. The flexspline teeth can be placed near the centre of a long hermetically sealed flexible cylindrical tube. The wave generator can be inside the tube, and, by its rotation, it can deflect the flexspline and produce a slow rotation of the encircling circular spline.

A rotary-to-linear version of the Harmonic Drive uses a screw and moves the control rod in a nuclear reactor head without mechanical contact through a sealed tube. Harmonic Drive systems are useful in increasing the output torque in gears used in milling, in manufacturing, and in machines that use robotic arms. They have been employed in a variety of applications, ranging from such low-cost consumer items as vending machines to sophisticated systems for military and aerospace use.

Harmonic drive gears are widely used in space applications, robotics, and precision positioning systems because of their attractive attributes including near-zero backlash, high speed reduction ratio, compact size, and small weight. They possess an inherent periodic positioning error known as kinematic error responsible for transmission performance degradation.

Have a clear understanding of the mechanisms of motion errors and their characterization. We report analytical and experimental results of motion errors using a dedicated study of harmonic drive test equipment. It is first shown that the error called kinematic error actually consists of a fundamental component, representing the "pure" kinematic error, colored by a second component arising from the inherent torsional flexibility of the harmonic drive gears.

The latter component explains the source of variability in published kinematic error profiles. The decomposition of the kinematic error into a basic component and a flexibility related component is demonstrated experimentally as well as analytically by matching a mathematical model to experimental data. We also characterize the dependence of the kinematic error on inertial load, gear assembly, and rotational speed.