Spatial Kinematic Analysis of Threaded Fastener Assembly

[+] Author and Article Information
Stephen Wiedmann

 Southwest Research Institute, 6220 Culebra Rd., San Antonio, TX 78238swiedmann@swri.org

Bob Sturges

Industrial & Systems Engineering, Virginia Tech, 100 Durham Hall, Blacksburg, VA 24061sturges@vt.edu

J. Mech. Des 128(1), 116-127 (Apr 26, 2005) (12 pages) doi:10.1115/1.2114909 History: Received May 18, 2004; Revised April 26, 2005

Compliant mechanisms for rigid part mating exist for prismatic geometries. A few instances are known of mechanisms to assemble screw threads. A comprehensive solution to this essentially geometric problem comprises at least three parts: parametric equations for nut and bolt contact in the critical starting phase of assembly, the possible space of motions between these parts during this phase, and the design space of compliant devices which accomplish the desired motions in the presence of friction and positional uncertainty. This work concentrates on the second part in which the threaded pair is modeled numerically, and contact tests are automated through software. Tessellated solid models were used during three-dimensional collision analysis to enumerate the approximate location of the initial contact point. The advent of a second contact point presented a more constrained contact state. Thus, the bolt is rotated about a vector defined by the initial two contact points until a third contact location was found. By analyzing the depth of intersection of the bolt into the nut as well as the vertical movement of the origin of the bolt reference frame, we determined that there are three types of contacts states present: unstable two-point, quasi-stable two-point, stable three point. The space of possible motions is bounded by these end conditions which will differ in detail depending upon the starting orientations. We investigated all potential orientations which obtain from a discretization of the roll, pitch, and yaw uncertainties, each of which has its own set of contact points. From this exhaustive examination, a full contact state history was determined, which lays the foundation for the design space of either compliant mechanisms or intelligent sensor-rich controls.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 2

Tessellated solid model—bolt and nut

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Figure 3

Types of bolt and nut triangle intersection

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Figure 4

Endpoints of intersecting line segment

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Figure 5

Definition of rotation angles

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Figure 6

Possible contact state configurations

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Figure 7

Depth change as a function of phase rotation for case 1

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Figure 8

Depth change as a function of phase rotation for case 2

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Figure 9

Depth change as a function of phase rotation for case 3

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Figure 10

Depth change as a function of phase rotation for case 4

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Figure 11

First contact state model

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Figure 1

Internal and external thread profiles

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Figure 21

Stable contact point locations (α=−4, β=0, ϕ=131)

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Figure 22

Relation of contact states to all angular conditions

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Figure 17

Coordinate frames at three-point contact

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Figure 12

Second contact state model

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Figure 13

Vector rotation angles

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Figure 18

Cyclic diagram to convert to bolt reference frame

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Figure 14

Coordinate frames at two-point contact

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Figure 15

Third contact state model

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Figure 19

Unstable contact point locations (α=4, β=0, ϕ=185)

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Figure 20

Quasi-stable contact point locations (α=4, β=4, ϕ=235)

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Figure 16

Cyclic diagram for third contact state model



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