Kinematics Of The 3 D Spatial Four Bar Linkage : Pseudographics A Computational Method

A pseudographical technique, in conjunction with an equation solving software, is used for an analysis of the kinematics of a 3-D spatial four bar linkage. Coordinates of position, velocity, and acceleration polygons are generated for a range of angles of the driving crank, and plots of output angular features versus input angle are provided. This work describes an alternative approach to vector 3-D kinematics, providing students with another perspective in linkage analysis. The author makes no claim that pseudographics is superior to an entirely vectorial solution, but rather tries to emphasize the utility of making a methodological option available. This concept of "option" is the rationale for the paper. In closing, the paper summarizes the advantages and disadvantages of pseudographics in comparison to current textbook approaches to 3-D mechanism kinematics. Computer codes are appended. Introduction. Previous work by the author on planar mechanism analysis and linkage dimensional optimization has demonstrated a computational method with the coined name "pseudographics". The efficacy of the commercial software employed for the technique has been discussed in these earlier papers. The present work extends the use of pseudographics to the kinematic analysis of a three dimensional mechanism. Single driving crank angle solutions for the 3-D spatial four bar linkage are very comprehensively presented in a number of current introductory texts on dynamics, and the data, as in Fig. 1, from a typical example problem are used to demonstrate pseudographics. The customary method for determination of angular velocities and accelerations in 3-D mechanisms is a vectorial one that students may find both tortuous and somewhat abstract. The current work attempts to circumvent many of these difficulties by replacing vector operations with a software aided calculation of the coordinates of the vertices of position, velocity, and acceleration diagrams for a range of motion of the driving crank. The method of pseudographics does not P ge 781.1 "Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright ” 2002, American Society for Engineering Education" offer any new concepts, but rather provides students with an optional tool in two and threedimensional kinematic analysis. An initial set of guesses is required for position, velocity and acceleration unknowns, and the corrected solutions are carried forward as the guessed results for the next angular position. While diagram drawing is not essential, simple figures do help in making the starting guesses. While the concepts are essentially vectorial, vector operations (cross, dot, mixed products) are not employed at all. The method offers an interesting reinforcement to the elegant, but more mathematically demanding, vector algebra approach. Students appreciate the strong physical connection to the mechanism that the pseudographical method provides less math, more graphics and visualization and those taking a course on 3-D kinematics should appreciate the confirmation of “traditional” solutions.