CATALOG DATA:
An in-depth study of the curvature theory of general planar one degree of freedom motion and the special case of first-order translations. Development of Fruedenstein’s equation. Applications to synthesis of one degree of freedom mechanisms for path tracking, rigid body guidance and function generation.REFERENCE BOOKS:
Roth, B., and Yang, A. T., Application of Instantaneous Invariants to the Analysis and Synthesis of Mechanisms, ASME J. of Engineering for Industry, pp. 97-102, 1977.Lorenc, S.J., Stanisic, M.M. and Hall, A.S., Application of Instantaneous Invariants to the Path Tracking Control Problem of Planar Two degree-of-Freedom Systems: A Singularity-Free Mapping of Trajectory Geometry, Mechanism and Machine Theory, vol. 30, no. 6, pp. 883-896, 1995
GOALS:
To teach students modern computer-based methods of synthesizing planar one degree-of-freedom mechanisms for the purposes of path-tracking, rigid-body guidance and function generation. Students are shown by examples how to identify these three types of problems and they are taught a systematic procedure for generating solutions. Mastery is demonstrated by four to five design projects and a few homework assignments.Topics:
- Overview of kinematic synthesis of mechanisms.
- Computer-based kinematic analysis of planar mechanisms.
i. The vector loop method and the kinematic coefficients.- Review of Taylor’s series expansion.
- Instantaneous kinematics of general planar one degree of freedom motion.
i. The canonical coordinate system of planar one degree of freedom motion.
ii. The instantaneous invariants of planar one degree of freedom motion.
iii. Kinematic geometry of planar one degree of freedom motion.
iv. Applications to synthesis of path tracking mechanisms.
v. Applications to synthesis of rigid-body guidance mechanisms.
vi. Applications to synthesis of function generating mechanisms.- Instantaneous first-order translations in planar one degree of freedom motion.
i. Applications to synthesis of rigid-body guidance mechanisms.
ii. Applications to synthesis of function generating mechanisms.- Fruedenstein’s Equation.
i. Applications to synthesis of function generating mechanisms.Practice and Assessment Methods:
To solve the design problems the students must write extensive computer programs. Checking their results also requires a computer program. The students complete at least four such design problems in the form of small projects. Students are required to communicate their results through a written report making good use of graphics. Performance is assessed by grading reports and homeworks.ABET category content as estimated by faculty member who prepared the course description:
Engineering Science: 1.5 credits or 50%
Engineering Design: 1.5 credits or 50%
Prepared by: Professor Michael Stanisic
Last Update: May 20, 2004
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comments, questions, and corrections to amedept@nd.edu