SECTION 8 ROTATION AND FRICTION Review the problem statement. Ask the students to enter the appropriate information about translational joints into the Constraints table. Demonstrate translational joints.

What is in this Section Euler Angles (Rotation Sequence) Precise Positioning: Rotate Modeling Friction Measures in LCS

Euler Angles (Rotation Sequence) Definition of Euler angles Adams/View uses three angles to perform three rotations about the axes of a coordinate system. These rotations can be space-fixed or body-fixed and are represented as Body [3 1 3], Space [1 2 3], and so on, where: 1 = x axis 2 = y axis 3 = z axis Default in Adams is Body [3 1 3]. For rotation about these axes, use the right hand rule

Euler Angles (Rotation Sequence) (Cont.) Example of body [3 1 3]: [90, -90, 180]: Example of space [3 1 3]: [90, -90, 180]: Give an overview of rotation sequences and explain that there are different types of rotation sequences. Do not review the slide in detail. Take questions individually. Mention other methods of determining orientation (Along axis, inplane). Demonstrate: You can use this demonstration or recreate first example above. Create two markers that are both initially aligned with global orientation (0,0,0). Assign one of the two markers the Body [313] orientation described above, as follows: Modify one of the marker’s orientation to be 90,0,0, and then compare the two. Then modify its orientation to be 90,-90,0, and then compare the two. Then modify it to have the third and final rotation, 90,-90,180.

Precise Positioning: Rotate To rotate objects about an axis in Adams/View, specify: The objects to rotate. The axis about which the objects are rotated. The angle through which the objects are rotated. Note: Be careful with the sign of the angle. Adams/View uses the right-hand rule. You can rotate several objects at once about the same axis. Demonstrate: Rotate an object. Use the Position: Rotate objects... tool in the tool stack in lower left side of the Main Toolbox. Then, rotate multiple objects at once using the select list. Question: In the figure, what information would you give Adams/View to rotate the objects? Answer: You could rotate either body, but, in this case, rotate the link (the lower part). Create a marker on the link on the edge closest to the cylinder, and rotate the link about the axis of the marker that runs along the long edge of the link. -45° (note negative sign)

Modeling Friction Joint friction can be applied to: Translational joints (Translational Joint, DOF Removed by, see Appendix A) Revolute joints Cylindrical joints Hooke/Universal joints Spherical joints Friction forces (Ff) Are independent of the contact area between two bodies. Act in a direction opposite to that of the relative velocity between the two bodies. Are proportional to the normal force (N) between the two bodies by a constant (μ). Ff = μN

Modeling Friction (Cont.) Phases that define friction forces Stiction Transition Dynamic Demonstrate: Add joint friction to any constraint. Point out that the images on the next page exaggerate the stiction phase to better illustrate it. Bending and torsional moments are beyond the scope of this course. Do not explain these. Demonstrate the Joint Friction dialog box using the online documentation. In the online documentation, use the global search tool to find Joints: adding Friction to, and explain: Stiction threshold velocity, max stiction displacement, and preloads. Go back to the module cover page to review the problem statement again, then continue.

Modeling Friction (Cont.) Idealized Case Stiction |Vrel| = 0 0 < μ < μs Transition 0 < |Vrel| = V1 μd < μ < μs Dynamic V1 < |Vrel| μ = μd Adams/Solver case Stiction |Vrel| < ΔVs Transition ΔVs < |Vrel| < 1.5ΔVs Dynamic 1.5ΔVs < |Vrel| Use the illustrations to identify stiction threshold velocity and relate it to the maximum stiction deformation.

Modeling Friction (Cont.) Effect of maximum deformation on friction Input forces to friction Always include preload and reaction force. Bending and torsional moment are possible (however, advanced uses of joint friction are beyond the scope of this course).

Measures in LCS Measures can be represented in: Example Global coordinate system (GCS) (default) A marker’s local coordinate system (LCS) Example When a ball falls due to gravity:

Measures in LCS (Cont.) ˆ ˆ Acceleration due to gravity in the GCS using symbols xg, ŷg, zg to represent the global x, y, and z components is: Acceleration due to gravity in MAR_1's coordinate system is: Demonstrate: Use a model in which you can use a reference marker in the Modify Measurement dialog box. The reference marker could be any marker in the model. It could be attached to the object being measured. Question: Compare the acceleration of a ball in the y-direction of two different CS. Why are they different? Answer: In the global case, all of the ball's acceleration is in the y-direction, and the acceleration in the x- and z-directions is zero. In MARKER_1's case, only a portion of the acceleration is in the y-direction, the remaining acceleration is in the z-direction, and the acceleration in the x-direction is zero.