The Practice of Engineering Dynamics. Ronald J. Anderson
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The first transformation (Equation 1.14) can be used with Equation 1.13 to show that,
(1.16)
This is the same result as that shown in Equation 1.9.
Similarly, the second transformation (Equation 1.15) can be used with Equation 1.9 to show that,
(1.17)
Expanding this yields,
(1.18)
This is the same result as that shown in Equation 1.13.
The transformations described in this example are typical of those used in dynamic analysis. Dynamicists are prone to using whatever coordinate system is appropriate at the time and, sometimes, there are many intermediate coordinate systems used in deriving the final system. Nevertheless, each coordinate system in the sequence must be right handed and must be generated by a simple plane rotation from the preceding system.
1.4 Two Dimensional Motion with Variable Length
Figure 1.4 shows a rigid body rotating in a plane about a fixed point
Figure 1.4 A slider in a slot.
Since the distance from
The angular velocity of the body is not specified in magnitude but the fact that the body rotates in a plane fixes the direction of the angular velocity to be
where
The position of
and, differentiating this, we find the velocity of
The acceleration of the slider relative to point
or
Since both the velocity
(1.21)
and
(1.22)
1.5 Three Dimensional Kinematics
Figure 1.5 shows a three degree of freedom robot. The horizontal arm