Mechanism State Matrices for Spatial Reconfigurable Mechanisms

This paper improves augmented mechanism state matrices by replacing joint code with screw system notation. The proposed substitution allows for a more specific description of the joints in the mechanism and the capability to describe both spatial and planar mechanisms. Examples are provided which elucidate the proposed approach

The Life and Impact of Daniel Alexander Payne

On Washington Street, across from McKnight Hall and adjacent to the Intercultural Resource Center, a sign stands in commemoration of the life and accomplishments of an African American who studied at the seminary from 1835 to 1837. The plaque reads: Daniel Alexander Payne (1811-1893). Born a free African American. He taught the colored people at this college, 1837, while a student at the Lutheran Seminary. A historian, he was elected bishop of the AME Church, 1852, and was president of Wilberforce University, 1863-76. What Payne was able to achieve in his life is matched by few of his contemporaries considering the fact that he was a black who grew up in Charleston, South Carolina. Believing that he was ordained by God, he became an educator and an ordained minister. Later in his life, Payne became the first African American president of a college when the African Methodist Church bought Wilberforce University in 1863. Daniel Payne, with his intellectual ideas, influenced the policy of the AME Church for years to come. The Gettysburg College Intercultural Resource Center claims that Pennsylvania College’s acceptance of Daniel Payne was “the first step at addressing cultural diversity at Gettysburg College.” Payne’s personal ambition and his influence in both the abolition movement and the education of black Americans present an example of a model citizen. Course Information: Course Title: HIST 300: Historical Method Academic Term: Spring 2006 Course Instructor: Dr. Michael J. Birkner \u2772 Hidden in Plain Sight is a collection of student papers on objects that are hidden in plain sight around the Gettysburg College campus. Topics range from the Glatfelter Hall gargoyles to the statue of Eisenhower and from historical markers to athletic accomplishments. You can download the paper in pdf format and click View Photo to see the image in greater detail.https://cupola.gettysburg.edu/hiddenpapers/1035/thumbnail.jp

Embeddings in the 3/4 range

We give a complete obstruction to turning an immersion of an m-dimensional manifold M in Euclidean n-space into an embedding when 3n>4m+4. It is a secondary obstruction, and exists only when the primary obstruction, due to Haefliger, vanishes. The obstruction lives in a twisted cobordism group, and its vanishing implies the existence of an embedding in the regular homotopy class of the given immersion in the range indicated. We use Goodwillie's calculus of functors, following Weiss, to help organize and prove the result.Comment: 33 pages, extensively rewritten due to incorporation of comments by the refere

Derivatives of the identity and generalizations of Milnor's invariants

We synthesize work of U. Koschorke on link maps and work of B. Johnson on the derivatives of the identity functor in homotopy theory. The result can be viewed in two ways: (1) As a generalization of Koschorke's "higher Hopf invariants", which themselves can be viewed as a generalization of Milnor's invariants of link maps in Euclidean space; and (2) As a stable range description, in terms of bordism, of the cross effects of the identity functor in homotopy theory evaluated at spheres. We also show how our generalized Milnor invariants fit into the framework of a multivariable manifold calculus of functors, as developed by the author and Voli\'{c}, which is itself a generalization of the single variable version due to Weiss and Goodwillie.Comment: 25 pages, accepted for publication by the Journal of Topolog