This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1882 edition. Excerpt: ...QS must be parallel to PR and the rotation about it must be 6. This translation will move P a length equal to QQ' along PR, and the rotation about QS will move P along an arc perpendicular to PR. Hence QQ' must equal PN and NF must be the chord of the arc. It follows that QS must lie on a plane ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1882 edition. Excerpt: ...QS must be parallel to PR and the rotation about it must be 6. This translation will move P a length equal to QQ' along PR, and the rotation about QS will move P along an arc perpendicular to PR. Hence QQ' must equal PN and NF must be the chord of the arc. It follows that QS must lie on a plane bisecting NP' at right angles and at a distance a from PR where NP' = 2a sin 5, or, which is more convenient, at a distance y from 0 the plane NPP' where NP' = 2y tan. The rotation 0 round QS is to bring to P' and is in the same direction as the rotation 6 round PR. Hence the distance y must be measured from the middle point of NP in the direction in which that middle point is moved by its rotation round PR. Having found the only possible position of QS, it remains to show that the displacement of Q is really along QS. The rotation 6 round PR will cause Q to describe an arc whose chord Qq is parallel to FN and equal to 2a sin. The chord Qq is therefore equal to NP', and the translation NF brings q back to its position at Q. Hence Q is only moved by the translation PN, i.e. Q is moved along QS. 226. It follows from this reasoning that any displacement of a body can be represented by a rotation about some straight line and a translation parallel to that straight line. This mode of constructing the displacement is called a screw. The straight line is sometimes called the central axis and sometimes the axis of the screw. The ratio of the translation to the angle of rotation is called the pitch of the screw. 227. The same displacement of a body cannot be constructed by two different screws. For if possible let there be two central axes AB, CD. Then AB and CD by Art. 220 are parallel. The displacement of any point Q on CD is found by turning the body...
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Add this copy of A Treatise On The Dynamics Of A System Of Rigid Bodies. to cart. $21.42, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of A Treatise On The Dynamics Of A System Of Rigid Bodies. to cart. $31.73, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of A Treatise On The Dynamics Of A System Of Rigid Bodies. to cart. $53.78, new condition, Sold by Booksplease rated 4.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2022 by Legare Street Press.
