Constraint


Symbol:
Identifier: Mechanics.Rotation.Constraint
Version: 3.6
File: Rotary.cat
Connectors: Mechanical Connector (rotational) ctr1 Connectable to elements of the Rotational Mechanics library
Mechanical Connector (rotational) ctr2 Connectable to elements of the Rotational Mechanics library
Parameters: Kind of Constraint kind
  • "Angle Difference"
  • "Velocity Difference"
  • "Displacement Function x2 = f(x1)"
  • "Velocity Function v2 = f(v1)"
  • "Displacement Function x1 = f(x2)"
  • "Velocity Function v1 = f(v2)"
  • "Set dphi to Initial Angular Diff. of Connectors"
Angular Difference phi only visible, if kind=="Angular Difference"
Speed Difference om only visible, if kind=="Speed Difference"
Angle Function phi2=f(phi1) f_phi1 only visible, if kind=="Angle Function phi2=f(phi1)"
Speed Function om2=f(om1) f_om1 only visible, if kind=="Speed Function om2 = f(om1)"
Angle Function phi1=f(phi2) f_phi2 only visible, if kind=="Angle Function phi1=f(phi2)"
Speed Function om1=f(om2) f_om2 only visible, if kind=="Speed Function om1 = f(om2)"
Switchable Constraint switchable Enables the possiblitiy to switch the element active or inactive using the boolean parameter con
Activated con Constant condition for activation ("true" or "false")
Results: Internal Torque Ti
External Power Pe
  • Vorgabe einer konstanten oder zeitveränderlichen kinematischen Zwangsbedingung zwischen zwei Körpern (Drehträgheiten) oder gegen Umgebung
  • Winkel- oder Drehzahldifferenz
  • Optional schaltbar zum Koppeln oder Entkoppeln von Subsystemen
  • Preset of a constant or time-varying kinematic constraint between two bodies (inertias) or against environment
  • Angle or speed difference
  • Option: Switchable for coupling or decoupling subsystems

Description:

This element allows to model constraints, rigid dependencies, or transformations between rotary motion and force quantities at two locations (connections) in the system under study.

The torques at the connectors of this element are balanced, i.e., T1 (torque at ctr1) equals -T2 (torque at ctr2). In practice this implies, that the element does not have any hidden supports to the environment. Consequently, if the speeds at ctr1 and ctr2 are different, the element acts as a power/energy source or sink. For the description of element types, which do not convert power, the Gear element (ideal rotary to rotary transformer, which has internal supports to the environment) can be used.

Parameters:

The Kind of Constraint of constraint is defined in the selection box kind and turns on the input field of the respective parameter. There are six constraint options:

  • "Angular Difference":
    By entering a value in the parameter field Angular Difference (phi) a twist angle between the two connectors of the element is defined. The element ensures the abidance of the constraint.
  • "Speed Difference":
    By entering a value in the parameter field Speed Difference (om) a speed deviation between the two connectors of the element is defined. The element ensures the abidance of the constraint.
  • 2x Angle Functions ("Displacement Function x2 = f(x1)" and "Displacement Function x1 = f(x2)":
    Using the settings Angle Function phi2=f(phi1) or Angle Function phi1=f(phi2) it becomes possible to describe the relation between the angles at ctr1 (phi1) and ctr2 (phi2) by arbitrary functions. The formulated expressions can contain numbers, variables, functions, and of course the two angle designators phi1 and phi2. Time-dependent relationships can be described using the system variable t. An expression could look like as follows: phi1+0.01*sin(2*pi*5*t).
  • 2x Speed Functions ("Velocity Function v2 = f(v1)" and "Velocity Function v1 = f(v2)"):
    Using the settings Speed Function om2=f(om1) or Speed Function om1=f(om2) it becomes possible to describe the relation between the speeds at ctr1 (om1) and ctr2 (om2) by arbitrary functions (in analogy to the Angle Function).
  • "Set dphi to Initial Angular Diff. of Connectors":
    This option sets a constant angle difference constraint. This angle difference (dphi) will be computed by the initial values of the connected structures (inertias, connections) at ctr1 and ctr2.

The checkbox Switchable Constraint enable the boolean parameter con. con allows to switch the element between active or inactive by setting a true or false condition. Using this option it is possible to couple or decouple two mechanical sub-systems.

Results:

  • The Internal TorqueTi of the element is available as a result variable for display and further processing. Its sign is defined according to the sign convention used for all elements in the mechanics libraries: A positive internal torque has an accelerating effect on components connected to ctr2 and a decelerating effect on components connected to ctr1 respectively (see the remarks for the External Torque for further details).
  • The Constraint also computes the power contributed by the constraint to the mechanical system:

Results:

  • If constraints are given in a form coordinate1 = f(coordinate2), the element can be included into the model with a 180° rotation, such that ctr1 is linked to coordinate 2 and ctr2 to coordinate 1 respectively. When entering the expression into the parameter dialog, phi1 or om1 must be used instead of coordinate 2.
  • If there appears an error message "Calculation of consistent initial values failed", it is recommended to check the initial conditions (see the chapter "Modeling/Control for Initial Values" in the User Manual) in the surroundings of the element and to correct them or free them (by "un-pinning" them) accordingly.