Editing Linkage (mechanical) (section)

==History==
[[Archimedes]]<ref>{{cite journal | last1 = Koetsier | first1 = T. | year = 1986 | title = From Kinematically Generated Curves to Instantaneous Invariants: Episodes in the History of Instantaneous Planar Kinematics | journal = Mechanism and Machine Theory | volume = 21 | issue = 6| pages = 489–498 | doi = 10.1016/0094-114x(86)90132-1 }}</ref> applied geometry to the study of the lever.  Into the 1500s the work of Archimedes and [[Hero of Alexandria]] were the primary sources of machine theory.  It was [[Leonardo da Vinci]] who brought an inventive energy to machines and mechanism.<ref>A. P. Usher, 1929, A History of Mechanical Inventions, Harvard University Press, (reprinted by Dover Publications 1968)</ref>

In the mid-1700s the [[Watt steam engine|steam engine]] was of growing importance, and [[James Watt]] realized that efficiency could be increased by using different cylinders for expansion and condensation of the steam.  This drove his search for a linkage that could transform rotation of a crank into a linear slide, and resulted in his discovery of what is called [[Watt's linkage]].  This led to the study of linkages that could generate straight lines, even if only approximately; and inspired the mathematician [[J. J. Sylvester]], who lectured on the [[Peaucellier linkage]], which generates an exact straight line from a rotating crank.<ref name="C. Moon, 2009">F. C. Moon, "History of the Dynamics of Machines and Mechanisms from Leonardo to Timoshenko," International Symposium on History of Machines and Mechanisms, (H. S. Yan and M. Ceccarelli, eds.), 2009. {{doi|10.1007/978-1-4020-9485-9-1}}</ref>

The work of Sylvester inspired [[Alfred Kempe|A. B. Kempe]], who showed that linkages for addition and multiplication could be assembled into a system that traced a given algebraic curve.<ref>A. B. Kempe, "On a general method of describing plane curves of the nth degree by linkwork," Proceedings of the London Mathematical Society, VII:213–216, 1876</ref>  Kempe's design procedure has inspired research at the intersection of geometry and computer science.<ref>{{cite journal | last1 = Jordan | first1 = D. | last2 = Steiner | first2 = M. | year = 1999 | title = Configuration Spaces of Mechanical Linkages | journal = [[Discrete & Computational Geometry]] | volume = 22 | issue = 2| pages = 297–315 | doi = 10.1007/pl00009462 | doi-access = free }}</ref><ref>R. Connelly and E. D. Demaine, "Geometry and Topology of Polygonal Linkages," Chapter 9, Handbook of discrete and computational geometry, ([[Jacob E. Goodman|J. E. Goodman]] and J. O'Rourke, eds.), CRC Press, 2004</ref>

In the late 1800s [[Franz Reuleaux|F. Reuleaux]], A. B. W. Kennedy, and [[Ludwig Burmester|L. Burmester]] formalized the analysis and synthesis of linkage systems using [[descriptive geometry]], and [[Pafnuty Chebyshev|P. L. Chebyshev]] introduced analytical techniques for the study and invention of linkages.<ref name="C. Moon, 2009"/>

In the mid-1900s [[Ferdinand Freudenstein|F. Freudenstein]] and G. N. Sandor<ref>{{cite journal | last1 = Freudenstein | first1 = F. | last2 = Sandor | first2 = G. N. | year = 1959 | title = Synthesis of Path Generating Mechanisms by Means of a Programmed Digital Computer | journal = Journal of Engineering for Industry| volume = 81 | issue = 2| pages = 159–168 | doi = 10.1115/1.4008283 }}</ref> used the newly developed digital computer to solve the loop equations of a linkage and determine its dimensions for a desired function, initiating the computer-aided design of linkages.  Within two decades these computer techniques were integral to the analysis of complex machine systems<ref>{{cite journal | last1 = Sheth | first1 = P. N. | last2 = Uicker | first2 = J. J. | year = 1972 | title = IMP (Integrated Mechanisms Program), A Computer-Aided Design Analysis system for Mechanisms and Linkages | journal = Journal of Engineering for Industry| volume = 94 | issue = 2| pages = 454–464 | doi = 10.1115/1.3428176 }}</ref><ref>C. H. Suh and C. W. Radcliffe, Kinematics and Mechanism Design, John Wiley, pp:458, 1978</ref> and the control of robot manipulators.<ref>R. P. Paul, Robot Manipulators: Mathematics, Programming and Control, MIT Press, 1981</ref>

R. E. Kaufman<ref>R. E. Kaufman and W. G. Maurer, "Interactive Linkage Synthesis on a Small Computer", ACM National Conference, Aug.3–5, 1971</ref><ref>A. J. Rubel and R. E. Kaufman, 1977, "KINSYN III: A New Human-Engineered System for Interactive Computer-aided Design of Planar Linkages," ASME Transactions, Journal of Engineering for Industry, May</ref> combined the computer's ability to rapidly compute the roots of polynomial equations with a graphical user interface to unite [[Ferdinand Freudenstein|Freudenstein's]] techniques with the geometrical methods of Reuleaux and [[Burmester's theory|Burmester]] and form ''KINSYN,'' an interactive computer graphics system for linkage design

The modern study of linkages includes the analysis and design of articulated systems that appear in robots, machine tools, and cable driven and tensegrity systems.  These techniques are also being applied to biological systems and even the study of proteins.