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## twenty-first-century geometry

###### Introducing the Precise Motion Technology

21Geo offers the Precise Motion Methodology which generates Motion Specialized Bearings (MSB).  The methodology takes as inputs the desired positions and rotations (X, Y, and rotation) of two components and generates a bearing that will support those motions.  Each of the inputs is a continuous degree of freedom, represented by an array of values for X, Y and rotation.

The resulting bearing surface will ensure constant contact with the two raceways throughout the range of motion.  The methodology also ensures the pin rolls and does not slide.  Finally, the contact points on the pin will oppose each other, throughout the range of motion, to prevent jams and sliding.

The pins need guides to ensure they stay in place.  The MSB Shown has chevron guides.  In normal operation, the guides are idle.  Power is transmitted through the raceway surfaces (blue in color).  Without the guides, the pin could work its way loose.

The MSB in above was designed so that the lower right component would move left to right smoothly.  The component in the upper left moves up and down such that the mechanical advantage for the overall system varies from 4 to 1 and 1 to 4.  Note how the upper left component moves slowly at the bottom and fast at the top.

The above example was designed as a learning aid.  Much more complex systems are possible.  The bearing can be used in both a looped process as shown the Precise Cycle examples and can be used in a back-and-forth mechanism.

MSB can be used for anything that moves. The Precise Motion Technology offers more flexibility for mechanical designers than any other mechanical paradigm.  Nothing else in mechanical engineering can match the flexibility.

The Details

As stated above, the methodology takes the description of motion, the pin start position, and the direction of rotation to generate a motion specialized bearing.  There are two steps to get the raceways surfaces resolved for low friction and opposing contact points.  The first step is to estimate the pin path and the resulting raceway surfaces.  21Geo has a routine to make that estimate that is good enough to use as input for the second pass.

The second pass measures the friction at every interval and the opposing angles at every point.  A numeric optimizer adjusts the pin path to virtually eliminate friction and ensures opposing contact points.  The second pass also resolves other necessary boundary conditions.  For instance, in the example below, the second pass resolves the criteria for the repeating patterns.

The below images are from the custom application designed to accomplish both passes.  The top images are a result of the first pass.  There are multiple examples highlighted where the conditions for the repeating pattern is not met.  Also, the close-up shows the guides not lining up.  The guide distance is constant so a misalignment would lead to dragging for the pin.

The lower images are after the second pass.  The repeating pattern boundary conditions have been met, and the contour between lobes is smooth.  The close-up also shows the guides aligning.  The friction has been virtually eliminated.

The lower images show dotted lines that represent trial pin paths and trial raceway surfaces.  The lowest was the original estimate.  There are few subsequent paths and a thin black line shows the final path.  The raceways surfaces are adjusted to match the changes in the pin path.

To learn how Continuous Geometry lowers upfront and operational costs for HVAC and refrigeration see our compressor case study.

To learn how Continuous Geometry lowers upfront and operational costs for engines, see our case study on engines.

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