About Interpolation of Time Increments

An excitation drives one or several commands in a mechanism. Values are specified for each command and for each time step of the simulation. If a time increment defined for an excitation differs from the time increment of the simulation, then the command values are interpolated based on the simulation time increment.

Time and command values are specified in a value table. Depending on the excitation type, the value table can be:

a design table (for law excitations)
a recorded excitation table (for recorded excitations).

If time increments from the value table and from the simulation differ, then the simulation adapts to the situation.


Initial Condition	Simulation Result
The first time increment from the value table exceeds the initial time increment of the simulation.	The mechanism remains at its nominal position until the simulation reaches the smallest increment in the value table.
The simulation extends past the final time increment of the value table.	The final value specified in the table is enforced until the simulation is over.
One or more of the time increments of the value table do not correspond to the time increments of the kinematic simulation.	The command value is interpolated based on the two closest time parameters in the value table.

The interpolation of command values only works if a value is specified for both the previous and subsequent increments in the value table. This may not be the case for interdependent commands, for which the values of one command depends on the values defined for the other.

The following examples provide more information on those two use cases.

Example of a Single Command

In this example, the command values in the table are defined according to five-second increments, starting at 5 seconds. However, the simulation runs in one-second increments, starting at 0 seconds.

Table 1. Value Table
`Excitation.1\Time(sec)`	5	10	15
`Excitation.1\Length(mm)`	5	7	12


Time Range	Behavior
From 0 to 4 seconds	The command remains at its nominal value (in this case, 1).
At 5, 10, and 15 seconds	The command value matches the value specified in the table. The command value is interpolated linearly between each of these increments.
After 15 seconds	The command value remains at the final value specified in the value table.

Example of Interdependent Commands

In this example, the value table defines two interdependent commands: the value of one angle can be determined in the mechanism based on the value of the other angle. The command values are defined according to two-second increments, while the simulation runs in one-second increments.

Table 2. Value Table
`Excitation.1\Time(sec)`	0	2	4	6	8	10
`Excitation.1\Angle(deg)`	30	40	50
`Excitation.2\Angle(deg)`				30	40	50

For each time range of the simulation, the command values are defined accordingly.


Time Range	Behavior
From 0 to 4 seconds	The values for Angle 1 match the values specified in the value table. The values for seconds 1 and 3 are interpolated linearly. The values for Angle 2 are calculated in the mechanism based on the values of Angle 1.
At 5 seconds	The assigned values in the table switch from Angle 1 to Angle 2. The command values cannot be interpolated. For the Angle 1 command, the upper bound for calculating the interpolation is missing. For the Angle 2 command, the lower bound for calculating the interpolation is missing. The mechanism keeps its last configuration.
From 6 to 10 seconds	The values for Angle 2 match the values specified in the value table. The values for seconds 7 and 9 are interpolated linearly. The values for Angle 1 are calculated in the mechanism based on the values of Angle 2.