7.3.2 Reaction

The Reaction function is used to convert the Lagrange multipliers that are returned by SolveMech into specific reaction forces and moments that are applied to each body by the constraints in the mechanism model.

The function for finding constraint reaction forces.

An option for Reaction.

To demonstrate the use of Reaction, loads are applied to the ladder-on-wall model that was redefined in Section 7.3.1.

Here are the load objects for the ladder-on-wall model.

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Only the first two loads are added to the model initially; the other load will be added later. The model can then be run with the Solution -> Static option to solve for the Lagrange multipliers.

Load 1 and load 2 are applied to the current model.

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Now run the model at T = 6.0.

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Because the Reaction function references constraints by number, names are given to each of the constraints for clarity.

Names are defined for each of the constraints in the model.

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The horizontal force at the bottom of the ladder that is required to hold the ladder in its current position is the reaction to constraint 1, the driving constraint. Note that the Y force and the moment sustained by the driving constraint are both zero, and always will be, because the driving constraint (RelativeX1) does not constrain motion in the Y or directions, therefore, it cannot sustain any load in those directions.

Here is the reaction to the driver.

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For the ladder to be in equilibrium, the force at the driver must be balanced by the force against the wall. Note that the Reaction function, like all other Mech output functions, returns a symbolic expression in terms of dependent variables.

Here is the reaction against the wall.

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Note that if a different point is chosen about which to calculate the reaction, only the moment is changed. A reaction force is not a function of the point about which the reaction is calculated, therefore, the choice of a calculation point never affects the force, only the moment.

Here is the reaction against the wall calculated about a point on the ground.

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Since there is no friction in this model, the sum of all of the vertical forces is applied to the floor.

Here is the reaction against the floor.

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When the applied moment, load 3, is added to the model, it shows up as added reaction force against the driver and the wall.

The moment that was previously defined is added to the model.

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Here is the reaction against the wall.

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