The development of analytic techniques and FORTRAN programs for the evaluation of plane motion mechanisms

Graduation date: 1965A mechanism is a constrained kinematic chain composed of\ud gears, links, cams, or the like. Mechanisms are the building blocks\ud of all machines, and, as such, their evaluation is of considerable\ud importance to the mechanical designer. Because the mathematical\ud analyses of systems with four or more moving members has been\ud prohibitively complex, the principal method of mechanism evaluation\ud has been graphical. With the development and widespread distribution\ud of high-speed digital computer systems, however, mathematical\ud methods for complex-linkage evaluation have become practicable.\ud Because of the somewhat universal nature of the digital computer\ud language called FORTRAN, it is possible for an analyst to develop\ud a system of analysis which not only he, but any other person as well,\ud may use. In this paper are developed analytic techniques and computer\ud programs which evaluate the principal class of mechanisms --\ud plane motion linkages with a single degree of freedom, employing\ud turning joints, and having either an angular or translational input\ud motion. The fundamental premise is that a link may be represented\ud by a complex vector, and a linkage may be represented by a set of\ud these vectors in the form of closed polygons. The position vectors,\ud which are known and are considered to be functions of time, sum to\ud zero about a closed path. There exist, in a single degree of freedom\ud linkage, one-half as many independent closed paths as n-Iinks free to\ud rotate (i.e., links which are neither the crank nor the frame). Therefore,\ud one-half-n independent vector sums may be written. By separating\ud the sums into their real and imaginary parts, n independent\ud equations result. The first and second time-derivatives of the n-set\ud provides two n-sets of linear algebraic equations. These two sets\ud are solved, by the computer, for the n-unknown angular rates and\ud the n-unknown angular accelerations. With these values of angular\ud kinematic quantities, the computer estimates the angular rotations\ud over a particular time interval. Through use of a simple iterative\ud process, these estimated angular values are improved. If the angular\ud transition is not large, convergence is rapid. After calculation of\ud angular rates and accelerations in this new position, the process is\ud repeated, as before, until the desired range of operation of the linkage\ud has been traversed. Having determined the linkage's angular kinematic values\ud for a particular position (or instant of time), the computer uses the\ud values to calculate the translational kinematic data of any specified\ud point on the linkage. The translational values are placed in an absolute\ud reference by using the drive-member frame pin as the datum and\ud summing the translational vector components to the desired point.\ud The mathematical system of equations and logic are validated\ud by the successful evaluation of an eleven-bar, ram-drive linkage\ud system,\ud It is acknowledged that these methods and the associated\ud computer programs, although a significant improvement over widely\ud practiced linkage evaluation methods, are but the first step in the use\ud of the digital computer in mechanical design. Work must also be done\ud to develop computer methods to assist the mechanical designers with\ud dynamic evaluation, stress analysis, bearing loading, space budgeting,\ud force analysis, and so forth