Constraint that maintains a fixed angle between the Z axes of two frames
This block represents a fixed angle between the Z-axes of the base and follower frames. This constraint allows the base and follower frames to translate and rotate with respect to each other, with the requirement that their Z axes maintain the angle that you specify. Use this constraint in conjunction with joint blocks.
The dialog box provides three predefined angle constraints. These include parallel (0°), anti-parallel (180°), and perpendicular (90°) constraints. A General option allows you to specify other constraint angles. By definition, the constraint angle falls in the range 0–180°.
The dialog box contains a Properties area with angle constraint options and parameters.
Select the method to use to specify the angle constraint. The default method is General.
|Parallel||Align base and follower frame +Z axes|
|Anti-Parallel||Align the base frame +Z axis with the follower frame -Z axis|
|Perpendicular||Make base and follower frame Z axes mutually orthogonal|
|General||Maintain base and follower frame Z axes at an angle that you specify|
Using the Angle Constraint block, you can fix the angle between the Z-axes of the Base and Follower port frames. The intersection of the two port frame Z-axes defines the vertex about which the constraint angle is defined. Mathematically, the constraint angle between the two axes follows from the scalar product of the associated basis vectors, with vector components taken with respect to a common reference frame:
In agreement with the definition, any two angles possessing the same cosine value represent the same constraint angle. For example, 45 deg and 315 deg represent the same constraint angle (cos (45 deg) = cos (315 deg) = 1/sqrt(2)). As a general rule, you can represent every constraint angle with a numerical value contained in the interval [0, 180] deg.
It is possible to constrain the angle between the two port frame Z-axes while varying the angle between the X- and Y-axes. The set of all possible rotations consistent with the constraint angle describes a conical surface whose center line coincides with the Z-axis of the Base port frame. Model topology, as well as joints and other kinematic constraints, can act to reduce the set of allowed rotations between the two constrained port frames.
The Angle Constraint block eliminates a single rotational degree of freedom between the two port frames. In the absence of other joints and constraints in the kinematic loop, the two port frames retain three translational and two rotational degrees of freedom with respect to each other. The large number of degrees of freedom between the port frames can produce unexpected assembly results when the Angle Constraint block is used as the sole constraint in a model. You can further constrain the port frames by adding Joint and Constraint blocks between appropriate frames.
The angle constraint must not conflict with joints and other constraints present in the same kinematic loop. For example, any angle constraint which violates the requirement that the Z-axes of the two port frames of a Revolute Joint block remain parallel at all times results in assembly and simulation errors.