Please select this link to open the Geogebra Book containing constructions of a number of interesting linkages. This is an introduction to the useful movement available with articulated systems.
Animations of linkage movement.
Mark Plecnik shows that six-bar function generators can be used to drive a serial chain and produce a realistic wing flapping gait. Using trajectories obtained through video analysis by researchers Bret W. Tobalske and Kenneth P. Dial, “Flight Kinematics of Black-billed Magpies and Pigeons Over A Wide Range of Speeds,” Mark constructed functions for the joints of the serial chain, designed the function generators, and animated the results. Select this link for more information on Mark Plecnik and his work.
Researchers at Disney Research Zurich provide yet an other design system with the goal of moving digital character design into physical form. This work by Vittorio Megaro (ETH Zurich) and Bernhard Thomaszewski (Disney Research Zürich) and their colleagues can be viewed as two-position synthesis of four-bar “joints” that connect bodies in a serial chain, which are then driven by a sequence of four-bar function generators. They 3D print the result to obtain a cartoon character that moves with the rotation of a crank. Select this link for more information.
Kaustubh Sonawale and Yang Liu worked together on this design study for a micro-mechanical motion amplifier. It is an interconnected set of three eight-bar linkages.
This animation was prepared by Yang Liu for a linkage designed by Kaustubh Sonawale. The eight-bar linkage guides the platform in the approximation to rectilinear motion.
[evp_embed_video url=”http://cast.oit.uci.edu/jmmccart/Rectilinear-Sixbar.mp4″ width=”500″ height=”350″]
This is an animation of a Watt I six-bar linkage with a translating link that does not rotate (select the video to begin the animation). This is obtained using GeoGebra to execute a construction described by E. A. Dijksman in his book Motion Geometry of Mechanisms.
Disney Research guides two degree-of-freedom open chains using the coupler curve of a geared five-bar linkage to obtain geared seven-bar and nine-bar linkages, which they use to move the front and rear legs of their Cyber Tiger. By connecting the driving gears of the four legs, they obtain a one degree-of-freedom system that animates the Cyber Tiger.
The computational design system uses an optimization routine to adjust the coupler curve of the five-bar linkage to approximate a given curve in order to guide the system in a desired movement. The results are terrific, and look a lot like the mechanical toys of the past. Select this link for more information.
Our paper Numerical Synthesis of Six-bar Linkages for Mechanical Computation provides the mathematical theory that underlies the synthesis of a six-bar linkage with an input-output relationship that approximates a specified function. This describes how the Stephenson III six-bar linkage that sets the elevation for a ballistic trajectory was designed.
This Stephenson III six-bar linkage sets the elevation of a ballistic trajectory to reach a specified distance downrange given an initial velocity of 500 m/s. This function is described in Computing Linkages by A. Svoboda (pg 285). Mark Plecnik obtained this linkage after evaluating almost 100,000 different designs.