9.3 Velocity and Acceleration CouplesCoupled systems are not limited to geometric conditions that involve only mechanism body location and orientation. Velocity and acceleration terms may be included in the conditions to be satisfied. However, the parameters that are varied in attempting to satisfy the conditions are assumed to be constant. Mech parameters never have nonzero derivatives. 9.3.1 Solving for Two ParametersTo demonstrate the use of coupled systems to satisfy higher-order conditions, the four-bar model developed in Section 9.1 is used again. In the following example, the lengths of the drive bar and the driven bar are adjusted to satisfy two geometric conditions that are specified in two different mechanism configurations. One of the conditions is a first-order expression, specifying a component of the velocity of a point.
In the following example, bar2 and bar3 are adjusted so that the X coordinate of point 3 on the center bar is 0.4 at T = 0.3, and the Y velocity of point 3 on the center bar is 6.0 at T = 0.1. Initial guesses are specified for each configuration, and the initial guess for configuration 1, which contains the velocity condition, includes velocity terms. Here are two initial guesses for the two configurations. This builds the CoupleSystem object. This solves the CoupleSystem object.
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The nested list of rules returned by SolveCouple has one complete solution for each of the two mechanism configurations. Note that SolveCouple automatically determined that a velocity solution was needed for the first configuration by the presence of first-order terms in the geometric condition. This shows that the desired goal has been achieved.
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9.3.2 Solving for Multiple ParametersThis last example of the use of coupled systems with velocity dependence uses two geometric conditions that are satisfied in one configuration, and one condition that is satisfied in another configuration. One of the conditions is an expression involving velocity.
bar2, bar3, and bar4 are adjusted so that the X coordinate of point 3 on the center bar is 0.4 at T = 0.3, the Y velocity of point 3 is 5.5, at T = 0.1, and the Y coordinate of point 2 on the center bar is 3.7, also at T = 0.1. Here are the current values of the coordinates that are to be specified.
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This builds the CoupleSystem object. This solves the CoupleSystem object.
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This shows that the conditions are now satisfied.
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