intRamp, the time integral of the ramping factorįurther examples of mappings, illustrating the use of mathematical functions and time-varying quantities, can be found on the curvilinear constraints examples page.
rampDotDot, the second time derivative of the ramping factor.
rampDot, the first time derivative of the ramping factor.
ramp, the current value of the ramping factor.
rampFinishTime, the simulation time at which the ramp becomes equal to one.
rampStartTime, the simulation time at which the ramp becomes non-zero.
t0, the simulation time at the start of the simulation.
OrcaFlex also has certain reserved symbols available for use in mappings. A (non-comprehensive) list of functions available via SymPy is available on the SymPy help pages. Some common constants, such as pi, are also pre-defined. It is important to note that these functions are defined within SymPy and act symbolically, rather than numerically. Many common mathematical functions are available to mappings, including $\sin$, $\cos$, $\tan$ and $\exp$. The magnitude of this rotation vector is the angle of rotation necessary to rotate the in-frame to the out-frame its direction gives the axis of rotation.Īs an example, consider constraining the motion of the out-frame to lie on the straight line $X$ These are defined in the same way as for a simple Cartesian constraint: $x$, $y$ and $z$ are the translational coordinates of the out-frame origin relative and with respect to the axes of the in-frame $Rx$, $Ry$ and $Rz$ are the components of a rotation vector, again expressed relative and with respect to the axes of the in-frame. We will illustrate this shortly with an example, but for now let us recall the six basic degrees of freedom of the constraint: $x$, $y$, $z$, $Rx$, $Ry$ and $Rz$. The number of user-specified coordinates corresponds to the number of degrees of freedom in which motion of the out-frame is possible: one user-specified coordinate corresponds to motion along a curve, two to motion on a surface, etc. The utility of curvilinear constraints comes from the ability to define a bespoke set of coordinates in which to model the motion of the out-frame relative to the in-frame. See Python Interface: Installation for more information on installing Python. It is necessary to have both Python and the Python SymPy module installed in order to use curvilinear constraints. Curvilinear constraints allow a wide class of generalised constraint problems to be modelled in OrcaFlex, such as restricting the motion of the out-frame to lie on an arbitrary curve or surface, mixed calculated and imposed motion, and dynamic release of the out-frame based upon user-specified criteria.