ME326-Mechanical Design-Exam 1

Kinematic Pair

A joint between 2 or more links

Is the Kurtzbach equation always correct in predicting how much mobility there is in a kinematic chain?

No, it is not always correct

What is the difference between a machine and a mechanism?

A mechanism performs motion, machine does work

Describe motion of a linear actuator

A carrier is on a long, threaded shaft. When the shaft turns, the carrier moves in a straight line.

If a mechanism has 4 links, how many kinematic inversion does it have?

4

What is the difference between kinematics and kinetics?

Kinematics is just motion and kinetics includes forces

In the Kurztbach equation: m=3(n-1)-2j_1-j_2

j_1 is number of lower pairs, j_2 is number of higher pairs, n is number of links, m is mobility

What is the mobility of this?

m=1

What does it mean if m<0?

Statically indeterminate (overconstrained)

What is kinematic inversion?

A variation of a closed kinematic chain where a different link is the frame

Grashof’s law is in the equation: s+l< p+q. What happens if Grashof’s Law is not true for a mechanism?

The crank cannot turn a full revolution

What is locus of a point?

The path that a point travels through

In a vector such as R_xy, what is y and what is x?

y is where the vector starts and x is where it ends (where the arrow is)

Write the equation for the position difference between Rpo and Rqo

Rpq=Rpo-Rqo

Is position dfference a vector?

Yes it is

In the following diagram describe what Rpo2 is in words

a) in your own words: A vector from second origin O2 to P

b) Technical term used in class: apparent position of P to observer 2

What is the difference between position and location?

Position just describes a vector to a point on the body with no orientation info, location gives enough information to specify every point on the body includes orientation info

Write the loop closure equation for this

Rao+Rba+Rbo=0

For the given location of B in the following slider-crank mechanism, how many postures are there?

Two

How many coordinates are required to define the position of a point in spherical coordinates?

Three

Write the equation or expression for the displacement difference between two points on an object that is purely translated from one position to another

ΔRpq=0

What is the difference between a particle and a point?

A point has no dimensions but a particle is finite

2-D motion is called

Planar

Is position a vector?

Yes

Is position difference dependent on path

No

What is posture of a rigid body

Location and orientation of coordinate system on the body relative to stationary or world coordinate system.

What is a loop closure equation?

Loop closure equation contains constraints on distances and allowed movements of a closed kinematic chain

True or False: Each link in a loop closure system is referenced in absolute coordinates

False

What coordinate are required to define the position of a point in 2-D polar coordinates?

r and θ

Is displacement always equal to distance traveled? Why or why not?

No. Displacement is independent of path. The path may be longer than the displacement but not shorter.

Define rotation in terms of displacement differene.

P as seen from Q is in a different position. For pure translation it would appear to be the same position.

Is linear velocity a vector?

Yes

In which coordinate system is absolute velocity measure?

Absolute or world coordinate system

Are all angular displacements vectors?

No

Give two examples of angular displacements that are vectors

Infinitesimally small rotations and parallel axis rotations

If you perform three orthogonal rotations of an object in different orders, will the final location always be the same?

No

Is angular velocity a vector?

Yes

Describe the right hand rule

Using your right hand, extend four fingers in the direction of the first vector, bend your fingers to align with the second orthogonal vector, and your thumb will be pointed toward the cross-product direction.

For the rotation of a rigid body shown in the diagram below, describe how angular velocity changes along the axis of rotation (shown coming out of the cone on the lower left)

It will not change

Write the equation for the velocity difference vector from Q to P

Vpq=Vp-Vq

For velocity analysis where two points are separated, can they be on the same body?

Yes

For velocity analysis where two points are coincident and on the same body, what result do you get?

Trivial answer Vp=Vq

If the speed of an object changes, does velocity always change?

Yes

What are the two components of linear acceleration?

Normal and Tangential

Write the basic acceleration difference equation for points P and Q in 2-D

Apq=Ap-Aq

Does acceleration appear the same to all observers?

No

If the velocity of an object changes, does the speed always change?

No

Write the equation for angular acceleration in terms of angular velocity

⍺=𝛚’-𝛚 / dt

The equation for the acceleration of P relative to Q is: Apq= 𝛚 x (𝛚 x Rpq) + ⍺ x Rpq. Which term is acceleration due to angular velocity?

𝛚 x (𝛚 x Rpq)

If a 5-bar mechanism has mobility=2 meaning it has multiple degrees of freedom, how many links must be driven to define the movement of all of the links?

Two

What is the difference between an offset and a radial follower?

In an offset follower, the follower axis is not in line with (does not interact) the cam rotation axis. In a radial follower, the two axes intersect

Name one of the four methods for ensuring that a cam follower always maintains contact.

Gravity, spring, constant breadth, dual or conjugate cams

What is the portion of a cam displacement where the follower is not moving?

Dwell

If the cam follower is moving up or down at a constant rate, what is the name of that path or profile?

Uniform

In a cam displacement diagram if y is displacement, what are y’,y’’, and y’’’?

Slope, curvature, and change of curvature

In a cam displacement diagram, what is y’ * omega?

velocity of follower

In a cam displacement diagram, what is y’’ * omega?

acceleration of follower

In a cam displacement diagram, what is y’’’ * omega?

jerk of follower

True or False: Low-speed cams can always be run at high speeds without problems. Explain

False. The simple profiles have abrupt changes in acceleration which can cause noise and vibration in the machine.