By Elisha Sacks
This booklet provides the configuration house technique for computer-aided layout of mechanisms with altering half contacts. Configuration area is an entire and compact geometric illustration of half motions and half interactions that helps the center mechanism layout initiatives of research, synthesis, and tolerancing. it's the first normal algorithmic therapy of the kinematics of upper pairs with altering contacts. it is going to support designers notice and proper layout flaws and unforeseen kinematic behaviors, as confirmed within the book's 4 case stories taken from undefined. After featuring the configuration area framework and algorithms for mechanism kinematics, the authors describe algorithms for kinematic research, tolerancing, and synthesis in accordance with configuration areas. The case reports persist with, illustrating the applying of the configuration area way to the research and layout of automobile, micro-mechanical, and optical mechanisms. Appendixes supply a catalog of higher-pair mechanisms and an outline of HIPAIR, an open resource C++ mechanical layout process that implements the various configuration area tools defined within the e-book, together with configuration area visualization and kinematic simulation. HIPAIR comes with an interactive graphical consumer interface and plenty of pattern mechanism enter records. The Configuration house strategy for Kinematic layout of Mechanisms could be a important source for college students, researchers, and engineers in mechanical engineering, computing device technology, and robotics.
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Extra resources for The Configuration Space Method for Kinematic Design of Mechanisms
Example text
1 Survey of kinematic pairs Degrees of freedom Geometry Volume Total ::;2 >2 planar Lever mechanisms 1 159 130 29 102 Gear mechanisms 180 174 6 559 495 Lever mechanisms 2 Cam mechanisms Total 56 164 Percentage 43 148 89% 13 94 140 40 136 402 157 10 114 64 11% fixed-axis 57 46 16 Planar spatial 37 50 103 370 28% 72% 66% Notes: The first column shows the total number of pairs. The following two columns show the number of pairs with two or fewer degrees of freedom, or with more than two. The fourth and fifth columns indicate the number of planar and spatial pairs.
Segment b has equation B x - (y B)2 0, vertices gb and hb, and vertex coordinates g: (1, 1) and h: (1, -1). The tangency equations are = = = = = = P: + (p¢)2 q! (q:)2 _ = = 0 0 RA[1, 2P¢lt RB[l, -2q:lt x = O. Each segment is split at (0,0) into two monotonic subsegments. The con tact inequalities for the two upper subsegments are and likewise for the other three pairs of subsegments. For a fixed-axis pair, we have five scalar equations in six unknowns: two degrees of freedom and the four components of the two contact points.
3 Boundary conditions: (a) line, (b-c) circle. where db nC . h: replaces (RBnC)·(RBh:) using the invariance of inner products under rotation. 2b-c shows the tangency condition for a circle, a, with radius Ta and center 0a, and a circle, b, with radius Tb and center 0b. 2b), the distance between the centers equals the sum of the radii: Ilob- oall Ta + Tb with 11· 11 denoting the vector norm II vii (v; + vi ) 1/2. 2c), the distance between the centers equals the difference of the radii, lIob- oall Tb- Ta, and Tb > Ta.