AbstractsComputer Science

A mechanism is a constrained kinematic chain composed of gears, links, cams, or the like. Mechanisms are the building blocks of all machines, and, as such, their evaluation is of considerable importance to the mechanical designer. Because the mathematical analyses of systems with four or more moving members has been prohibitively complex, the principal method of mechanism evaluation has been graphical. With the development and widespread distribution of high-speed digital computer systems, however, mathematical methods for complex-linkage evaluation have become practicable. Because of the somewhat universal nature of the digital computer language called FORTRAN, it is possible for an analyst to develop a system of analysis which not only he, but any other person as well, may use. In this paper are developed analytic techniques and computer programs which evaluate the principal class of mechanisms  – plane motion linkages with a single degree of freedom, employing turning joints, and having either an angular or translational input motion. The fundamental premise is that a link may be represented by a complex vector, and a linkage may be represented by a set of these vectors in the form of closed polygons. The position vectors, which are known and are considered to be functions of time, sum to zero about a closed path. There exist, in a single degree of freedom linkage, one-half as many independent closed paths as n-Iinks free to rotate (i.e., links which are neither the crank nor the frame). Therefore, one-half-n independent vector sums may be written. By separating the sums into their real and imaginary parts, n independent equations result. The first and second time-derivatives of the n-set provides two n-sets of linear algebraic equations. These two sets are solved, by the computer, for the n-unknown angular rates and the n-unknown angular accelerations. With these values of angular kinematic quantities, the computer estimates the angular rotations over a particular time interval. Through use of a simple iterative process, these estimated angular values are improved. If the angular transition is not large, convergence is rapid. After calculation of angular rates and accelerations in this new position, the process is repeated, as before, until the desired range of operation of the linkage has been traversed. Having determined the linkage's angular kinematic values for a particular position (or instant of time), the computer uses the values to calculate the translational kinematic data of any specified point on the linkage. The translational values are placed in an absolute reference by using the drive-member frame pin as the datum and summing the translational vector components to the desired point. The mathematical system of equations and logic are validated by the successful evaluation of an eleven-bar, ram-drive linkage system, It is acknowledged that these methods and the associated computer programs, although a significant improvement over widely practiced linkage…