lecture 11 12 ch04 instant center
DESCRIPTION
Brief presentation on finding the instant center of a mechanism(s)TRANSCRIPT
MAE 364: Instant Centers JT
Every pair of links, even if they are not directly connected to each other, have an instant center.
Then, what is an instant center for a pair of links?Two coincident points (two points, each corresponding to a link, lying on top of each other)
These points will have the same velocity Magnitude Direction
Instant Center
Link 2 Link 3
P
VP2
VP3The instant center ‘P’ shown in the figure will be labelled as
MAE 364: Instant Centers JT
Associated with Joints:Revolute (Pin) Joints Instant center is located at the joint.
Prismatic (Translational) Joints Instant center is located at the center of curvature of the
path of the prismatic link.
Direct Contact JointsInstant center is located somewhere along the common
normal to the direct contact point.
Rolling Direct Contact Joints Assumed to behave like a revolute joint Hence, instant center located at rolling direct contact joint
Primary Instant Centers
MAE 364: Instant Centers JT
Instant center is located at the revolute joint.
Revolute (Pin) Joint
Primary instant center
Link 5
Link 4
MAE 364: Instant Centers JT
Instant center is located at the center of the curvature of the path of the prismatic link.
Prismatic (Translational) Joints
∞
Center of curvature of
link 1
For a rectilinear path, the
instant center is located at
infinity, perpendicular to the path.
MAE 364: Instant Centers JT
Instant center is located somewhere along the common normal to the direct contact point.
Direct Contact Joints
Slide Only
∞ ?
Rotate and Slide
Becomes a prismatic
joint
MAE 364: Instant Centers JT
Instant center is located at the rolling direct contact joint.
Rolling Direct Contact Joints
(Pure) Rolling[Zero velocity
point]
Instant center located at joint
MAE 364: Instant Centers JT
Associated with Joints:Revolute (Pin) Joints Instant center is located at the joint.
Prismatic (Translational) Joints Instant center is located at the center of curvature of the
path of the prismatic link.
Direct Contact JointsInstant center is located somewhere along the common
normal to the direct contact point.
Rolling Direct Contact Joints Assumed to behave like a revolute joint Hence, instant center located at rolling direct contact joint
Primary Instant Centers
MAE 364: Instant Centers JT
If a kinematic mechanism has n number of links.
Then, the number of instant centers, N, that mechanism has got is given by the below equation:
Number of Instant Centers
2
)1(
nnN
MAE 364: Instant Centers JT
Explained on White-Board In-Class
Star Diagram (Secondary Instant Centers)
MAE 364: Instant Centers JT
Used to find the secondary instant centers.
Kennedy’s Theorem: For bodies 1, 2, and 3, the instant centers 12, 13, and 23 are collinear.
Kennedy’s Theorem
The third unknown instant
center 23 will lie on this line
MAE 364: Instant Centers JT
Exam 1 (10/07/2014)1 question: Mass moment of inertia (Ch 17)1 question: Balancing of masses (Ch 19)# questions: Degrees of freedom (Ch 1)Between 3-5 DF problems.
1 question: Motion & Relative motion (Ch 2)Will have sub-questions.
1 question: Line of transmission (Ch 2)# questions: Four bar mechanisms (Ch 3)Will be a few questions similar to quiz 4.
No class on Thursday (09/25/2014).
Conclusion