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Linkage Synthesis Theory
The mathematical synthesis of linkage movement provides a powerful tool for invention. However, linkage synthesis procedures can yield defective designs, because the specified task may not have a useful solution.
The search for successful tasks can be discouraging, particularly if the resulting linkages are too big, too small, or otherwise unsatisfactory. To address this problem, we are working to automate the search and evaluation process for four-bar linkage synthesis.
Here we present Mathematica notebooks that find defect-free four-bar linkage designs:
Five-Position Synthesis of a Four-bar Linkage
Here we show a four-bar linkage designed to guide the coupler through five required task positions.
Please download and try our updated Mathematica notebook: Five-Position Synthesis. It searches in the vicinity of the required task for sets of positions that yield defect-free four-bar linkages. It may download as textfile so remove the .txt extension, then it should be readable by Mathematica.
Here is video capture that shows the operation of this notebook.
If you have any problems or advice, please contact me.
Synthesis of a Constraint for an Existing RR Serial Chain
Synthesis of an RR Constraint
An important technique in kinematic synthesis is the design of an RR constraint that controls the movement of two joints of an existing serial chain. For a given RR serial chain, like OA shown above, we can specify its movement through five required task positions. This provides the information needed to design an RR constraint, GW above, that ensures the system moves through the required task positions.
This technique is called function generation in the kinematics synthesis literature, because the synthesized RR constraint maintains a specified relationship between the joint angles alpha and beta at joints O and A.
Select this link to download our Mathematica notebook: RR-Constraint Synthesis. It uses a given RR chain and the associated task to determine tolerance zones, where it searches for defect-free designs. As above, this file may download as text file so remove the .txt extension, then it should be readable by Mathematica. If you have any questions, please contact me.