Kinematics table method

The kinematics table, shown in Table 7.1, introduces a method (referred to within this chapter as the table method) for efficiently managing the mathematics involved in analyzing multibody and multiple coordinate system problems, and can be used in either the Lagrangian or the Newton-Euler approach. A schematic diagram, which defines an inertial or body-fixed coordinate system, must accompany every kinematics table. The purpose of the schematic is to identify the point on the body at which the absolute velocity and acceleration is to be determined. The corresponding schematic for Table 7.1 is shown in Fig. 7.7. 

For a multibody system, each body would require a kinematics table and a corresponding schematic. The following examples illustrate the steps required for solving problems by the table method. Note that one example includes the expressions for acceleration to demonstrate the use of the table method with the Newton-Euler approach, while all other examples consider only the velocity. 

Determine the kinematic viscosity of the oil Use Fig. 6.1 and Table 6.2 or the Hydraulic Institute—Pipe Friction Manual kinematic viscosity and Reynolds number chart to determine the kinematic viscosity of the liquid. Enter Table 6.2 at kerosene and find the coordinates as X = 10.2, Y = 16.9. Using these coordinates, enter Fig. 6.1 and find the absolute viscosity of kerosene at 65°F as 2.4 cP. Using the method of Example 6.2, the kinematic viscosity, in cSt, equals absolute viscosity, cP/specific gravity of the liquid = 2.4/0.813 = 2.95 cSt. This value agrees closely with that given in the Pipe Friction Manual. 

A review of the literature reveals that previous finite-element analyses of adhesive joints were either based on simplified theoretical models or the analyses themselves did not exploit the full potential of the finite-element method. Also, several investigations involving finite-element analyses of the same adhesive joint have reported apparent contradictory conclusions about the variations of stresses in the joint.(24,36) while the computer program VISTA looks promising (see Table 1), its nonlinear viscoelastic capability is limited to Knauss and Emri.(28) Recently, Reddy and Roy(E2) (see also References 37 and 38) developed a computer program, called NOVA, based on the updated Lagrangian formulation of the kinematics of deformation of a two-dimensional continuum and Schapery s(26) nonlinear viscoelastic model. The free-volume model of Knauss and Emri(28) can be obtained as a degenerate model from Schapery s model. 

The range of kinematic viscorities covered by this test method is from 0.2 to 300 0(X) mmVs (see Table Al.l) at all temperatures (see 6.3 and 6.4). The precision has only been determined for those materi kinematic viscosity ranges and temperatures as shown in the footnotes to the precision section. 

X5.2 A detailed procedure for the measurement of the ice point and recalibration of thermometers is described in 6.5 of Test Method E 77. The suggestions in the following sections of this appendix are given specifically for the mercury-in-glass kinematic viscosity thermometers described in Table X4.2, and may not apply to other thermometers. 

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