Dr. Jagadeep Thota

MAE 364Kinematics and Dynamics of Machines

Chapter 4:Instant Centers

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

Example 1: Instant Centers 1

2

3

5

412

34

45

13 ∞

1523?

23

14

35

2524

MAE 364: Instant Centers JT

Example 1: Instant Centers

12

34

45

13 ∞

15

23

14

35

2524

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

MAE 364: Instant Centers JT

Solved on White-Board In-Class

Example 2: Instant Centers

MAE 364: Instant Centers JT

Example 3: Instant CentersSolved on White-Board In-Class