Catalog Data:
A course teaching the analysis and synthesis of planar, sperical and spatial mechanisms. Topics include: Vectors, analysis of planar mechanisms, design of cams, gear tooth geometry, analysis of transmissions, synthesis of planar mechanisms, direction cosine matrices, analysis of spherical mechanisms, homogeneous transformations and analysis of spatial mechanisms.

Prerequisites:
AME 20222, MATH 20580

Textbook:
None, Instructor notes and class notes only.

Course Objectives:
To teach students both graphical and analytical (computer based) methods of position analysis of planar, spherical, and spatial mechanisms. To teach analytical methods of cam design. To develop the involute tooth profite and analyze transmissions. To introduce students to dimensional-syntheses of planar mechanisms.

Topics Covered:
a. Introduction to mechanisms and machines.
b. Graphical Analysis of Planar Mechanisms

1. Skeleton Diagrams
2. Gruebler's Criterion
3. Graphical position analysis
4. Limit positions, dead positions, mechanical advantage
5. Grashof's Criterion
6. Instantaneous Centers

c. Analytical Methods in Planar Mechanisms

1. Position, velocity and acceleration analysis of mechanisms via the vector loop method
2. Newton-Raphson method and programming solutions
3. Displacement diagrams
4. Design of cams

d. Theory of Gearing

1. The involute tooth geometry
2. Simple gear trains
3. Planetary gear trains
4. Automotive transmissions, differentials, and transaxles
5. Gear forces

e. Synthesis of Planar Mechanisms

1. Synthesis of four bar mechanisms for rigid body guidance through four and five positions
2. Freudenstein’s equation

f. Analysis of Sperical and Spatial Mechanisms

1. Homogeneous transformations
2. Planar mechanism analysis via homogeneous transformations
3. Spherical mechanism analysis via homogeneous transformations
4. Spatial mechanism analysis via homogeneous transformations

Schedule:
Course meets for fifty minutes, three times weekly, for fourteen weeks

Contribution to Professional Component:
50% engineering science and 50% engineering design.

Contribution to Program Learning Outcomes and Assessment:

Outcome criterion	Topic	Student’s previous knowledge	Direct measures of outcome
(a) Ability to apply basic knowlege	Be able to apply: 1. vectors 2. product and chain rules of differentiation 3. matrix algebra, all to analyze mechanisms	MATH 10550, MATH 10560, MATH 20550, MATH 20580, AME 20221, AME 20222	Graded homeworks, projects and exams
c. Design a system component or product	Be able to design: 1. cams, 2. guiding mechanisms, and 3. fucntion generators	None	Graded homeworks, projects and exams
k. Use engineering tools	Be able to write extensive computer programs to analyze and synthesize mechanisms and display results graphically	EG 10111, EG 10112, AME 20214, AME 20212	Graded homeworks and projects

Prepared by: Michael M. Stanisic May 25, 2006

Direct comments, questions, and corrections to amedept@nd.edu