# FixedRotation

Fixed translation followed by a fixed rotation of frame_b with respect to frame_a

# Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Component for a fixed translation and fixed rotation of frame_b with respect to frame_a, i.e., the relationship between connectors frame_a and frame_b remains constant. There are several possibilities to define the orientation of frame_b with respect to frame_a:

• Planar rotation along axis 'n' (that is fixed and resolved in frame_a) with a fixed angle 'angle'.
• Vectors n_x and n_y that are directed along the corresponding axes direction of frame_b and are resolved in frame_a (if n_y is not orthogonal to n_x, the y-axis of frame_b is selected such that it is orthogonal to n_x and in the plane of n_x and n_y).
• Sequence of three planar axes rotations. For example, "sequence = {1,2,3}" and "angles = {90, 45, -90}" means to rotate frame_a around the x axis with 90 degrees, around the new y axis with 45 degrees and around the new z axis around -90 degrees to arrive at frame_b. Note, that sequence={1,2,3} is the Cardan angle sequence and sequence = {3,1,3} is the Euler angle sequence.

By default, this component is visualized by a cylinder connecting frame_a and frame_b, as shown in the figure below. In this figure frame_b is rotated along the z-axis of frame_a with 60 degree. Note, that the two visualized frames are not part of the component animation and that the animation may be switched off via parameter animation = false.

# Parameters (18)

animation Value: true Type: Boolean Description: = true, if animation shall be enabled Value: {0, 0, 0} Type: Position[3] (m) Description: Vector from frame_a to frame_b resolved in frame_a Value: Modelica.Mechanics.MultiBody.Types.RotationTypes.RotationAxis Type: RotationTypes Description: Type of rotation description Value: {1, 0, 0} Type: Axis Description: Axis of rotation in frame_a (= same as in frame_b) Value: 0 Type: Angle_deg (°) Description: Angle to rotate frame_a around axis n into frame_b Value: {1, 0, 0} Type: Axis Description: Vector along x-axis of frame_b resolved in frame_a Value: {0, 1, 0} Type: Axis Description: Vector along y-axis of frame_b resolved in frame_a Value: {1, 2, 3} Type: RotationSequence Description: Sequence of rotations Value: {0, 0, 0} Type: Angle_deg[3] (°) Description: Rotation angles around the axes defined in 'sequence' Value: "cylinder" Type: ShapeType Description: Type of shape Value: {0, 0, 0} Type: Position[3] (m) Description: Vector from frame_a to shape origin, resolved in frame_a Value: to_unit1(r - r_shape) Type: Axis Description: Vector in length direction of shape, resolved in frame_a Value: {0, 1, 0} Type: Axis Description: Vector in width direction of shape, resolved in frame_a Value: Modelica.Math.Vectors.length(r - r_shape) Type: Length (m) Description: Length of shape Value: length / world.defaultWidthFraction Type: Distance (m) Description: Width of shape Value: width Type: Distance (m) Description: Height of shape Value: 0.0 Type: ShapeExtra Description: Additional parameter depending on shapeType (see docu of Visualizers.Advanced.Shape) Value: if rotationType == Types.RotationTypes.RotationAxis then Frames.planarRotation(Modelica.Math.Vectors.normalizeWithAssert(n), Cv.from_deg(angle), 0) else if rotationType == Types.RotationTypes.TwoAxesVectors then Frames.from_nxy(n_x, n_y) else Frames.axesRotations(sequence, Cv.from_deg(angles), zeros(3)) Type: Orientation Description: Fixed rotation object from frame_a to frame_b

# Inputs (2)

color Default Value: Modelica.Mechanics.MultiBody.Types.Defaults.RodColor Type: Color Description: Color of shape Default Value: world.defaultSpecularCoefficient Type: SpecularCoefficient Description: Reflection of ambient light (= 0: light is completely absorbed)

# Connectors (2)

frame_a Type: Frame_a Description: Coordinate system fixed to the component with one cut-force and cut-torque Type: Frame_b Description: Coordinate system fixed to the component with one cut-force and cut-torque

# Components (4)

R_rel Type: Orientation Description: Fixed rotation object from frame_a to frame_b Type: World Type: Orientation Description: Inverse of R_rel (rotate from frame_b to frame_a) Type: Shape

# Used in Examples (6)

 ForceAndTorque Modelica.Mechanics.MultiBody.Examples.Elementary Demonstrate usage of ForceAndTorque element GyroscopicEffects Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects Demonstrates that a cylindrical body can be replaced by Rotor1D model PrismaticConstraint Modelica.Mechanics.MultiBody.Examples.Constraints Body attached by one spring and two prismatic joints or constrained to environment RevoluteConstraint Modelica.Mechanics.MultiBody.Examples.Constraints Body attached by one spring and revolute joint or constrained to environment SphericalConstraint Modelica.Mechanics.MultiBody.Examples.Constraints Body attached by one spring and spherical joint or constrained to environment UniversalConstraint Modelica.Mechanics.MultiBody.Examples.Constraints Body attached by one spring and universal joint or constrained to environment

# Used in Components (2)

 Cylinder Modelica.Mechanics.MultiBody.Examples.Loops.Utilities Cylinder with rod and crank of a combustion engine CylinderBase Modelica.Mechanics.MultiBody.Examples.Loops.Utilities One cylinder with analytic handling of kinematic loop