Dynamics of Machinery Flashcards
Describe mobility or DoF
Total number of independent coordinates.
(e.g. Airplane ~ x,y,z translation; roll, pitch, yaw rotation)
Also: number of control inputs
What is a link?
A rigid (or flexible) body with at least two nodes.
What is a joint?
A connection between two or more links.
A joint constrains or restricts motion
4 classifications of joints:
- Lower Pair
- Higher Pair
- Full Joint
- Half Joint
Define Lower Pair:
A Joint with a surface contact. (e.g. Pin in hole/rotary Joint, slider in slot/prismatic Joint)
Alt. Def’n:
joints with surface contact (as with a pin surrounded by a hole) (1 DoF)
Define Higher Pair:
A Joint with point or line contact. (e.g. Pin in slot, link against plane, disk on plane with rolling and slipping) (a joint that can have 2 or more DoF)
Define Full Joint:
It may be a lower Pair such as pin connection or higher Pair such as disk rolling on plane without slipping
DoF = 1
Define Half Joint:
Must be a higher Pair such as pin in slot, roll-slide Joint, disk on plane with rolling and slipping
Define Kinematic Chain:
Assemblage of links and joints interconnected to provide a controlled output motion in response to a supplied input motion.
Define Mechanism:
Kinematic chain in which at least one link is grounded.
Define Crank/Rocker/Coupler for a four-bar linkage:
Crank: link in pure rotation that can make a full revolution.
Rocker: link in pure rotation but oscillates.
Coupler: link that connects crank and rocker with complex motion.
Define Dyad:
A pair of binary links and one Joint. Typically used (in our case) to make a linkage a Grashof Linkage
Gruebler’s Equation:
M = 3L - 2J1 - J2 - 3
L: number of links
J1: number of full joints
J2: number of 1/2 joints
What makes a structure? What makes a pre-loaded structure?
DoF = 0
DoF < 0
Grashof Condition:
At least one link can make a full revolution.
S + L <= P + Q
3 classes of Grashof:
Class I: S + L < P + Q (kinematic chain)
Class II: S + L > P + Q (non-Grashof)
Class III: S + L = P + Q
What are the 3 named Inversions of Class 1?
Crank-Rocker - grounding either link adjacent to the shortest.
Double Crank - grounding shortest link.
Double Rocker - grounding link opposite to the shortest.
Inversions of Class II are all of what type?
Triple Rocker - where no link can fully rotate
Inversions of Class III are made up of what two types of linkage?
Double cranks and crank rockers.
Typically parallelogram and antiparallelogram
How to we define work in Dynamics of Machinery?
A product of angular displacement and torque.
What is qualitative synthesis?
Solutions without a well defined algorithm.
What is Quantitative synthesis?
Uses a set of well defined equations to form a solution.
What is Type Synthesis?
Defines an appropriate type of mechanism, a form of qualitative synthesis.
What is Function Generation?
Correlation between input motion and output motion.
Define Path Generation:
Control a point in the plane to follow a path.
Define Motion Generation:
Control of a line in a plane that assumes a set of sequential positions.
What is a toggle?
When two links become collinear
How many toggle points does double/triple Rocker have?
At least 2 positions that assume a triangle
Label two types of toggles.
Extended Collinear -
Overlapping Collinear -
What is dwell mechanism?
An intermittent motion Mechanism which alternates forward and return motion with holding positions.
What is a pseudo arc?
(To be continued…)
Define Transmission Angle:
The angle between the output link and the coupler (mu is always less than 90 degrees)
What is Kennedys Rule?
Any three bodies in plane motion will have exactly 3 instant centers, and they will lie on the same straight line.
In the case where we have clearance between the pin and the hole in a pin connection ~ what type of joint do we have?
higher pair, half joint
NOTE: if there is any clearance between pin and hole, the contact is considered line contact as the pin only contacts one side of the hole.
What are the 6 possible lower pairs and their DoF?
Revolute = 1, Prismatic (translating slider-joint) = 1, Helical (Screw) = 1, Cylindrical = 2, Spherical = 3, Planar (Flat) = 3
What are the two forms of planar joints with 1 DoF?
- Translating (prismatic) slider joint
- Rotating (revolute) pin joint
These are full joints and are lower pairs.
A Revolute joint in a loop is replaced by a prismatic (slider) joint. If the loop contains two revolute joints after the replacement, what is the DoF shift?
0; a revolute joint can be replaced by a prismatic joint with no change to DoF provided that at least two revolute joints remain.
A full joint is replaced by a half joint. What is he DoF shift?
+1; Increases by 1.
If all revolute joints are replaced by prismatic joints, what will be the resulting DoF?
2
What is the effect on DoF by removing one link?
-1; the total DoF will be reduced by one.
What is the chordal length for an output rocker?
The total length of the distance between the extreme positions for the joint that connects the coupler and the Rocker.
If the Crank center 02 is located off of the extended chord of an output Rocker ~ the mechanism is called…?
Quick-Return/Quick-Forward
What is dwell?
Zero output motion given some nonzero input motion
If theta = 4t^2. What can be said about the angular acceleration?
Constant at 8 rad/s^2
For the following, name the type of fourbar linkage and the class:
G = 7 L2 = 4 L3 = 2 L4 = 6
Grashof, Class 1, Double Rocker inversion
Choose the fourbar linkage (by educated guess) that has the largest minimum transmission angle. Also, which type of linkages are these?
1) G = 6 , L2 = 4 , L3 = 7 , L4 = 6;
2) G = 8 , L2 = 3 , L3 = 6 , L4 = 6
We choose 2 because it has the largest ground. It is a Class 1 Grashof Crank Rocker.
In general (rule of thumb): the fourbar with the largest ground link suggests that the minimum transmission angle is the largest of the compared linkages.
When seeking the minimum transmission angle, which configurations are considered?
Overlapping and extended. L2 (crank) is collinear with L1 (ground).
When considering maximum Rocker motion, which configurations are considered? (4-bar)
When the Crank and coupler are collinear. Forward, and return.
Which link is grounded to make a class 1 crank rocker inversion?
Either link closest to the shortest is grounded.
Which link is grounded to make a class 1 double rocker inversion?
Ground the link that is opposite to the shortest.
Which link is grounded to make a class 1 double crank inversion?
Ground the shortest link.
For the following, name the type of fourbar linkage and the class:
G = 6 L2 = 8 L3 = 6 L4 = 5
Non-Grashof, Class 2, Triple Rocker
For the following, name the type of fourbar linkage and the class:
G = 6 L2 = 4 L3 = 6 L4 = 7
Grashof, Class 1, Crank Rocker inversion
For the following, name the type of fourbar linkage and the class:
G = 4 L2 = 6 L3 = 6 L4 = 6
Grashof, Class 1, Double Crank Inversion
For the following, name the type of fourbar linkage and the class:
G = 8 L2 = 3 L3 = 6 L4 = 6
Grashof, Class 1, Crank Rocker Inversion
For the following, name the type of fourbar linkage and the class:
G = 6 L2 = 4 L3 = 6 L4 = 4
Grashof, Class 3, Double Crank
For the following, name the type of fourbar linkage and the class:
G = 8 L2 = 3 L3 = 6 L4 = 4
Non-Grashof, Class 2, Triple Rocker
What is the maximum possible transmission angle in a four-bar linkage system (in degrees)?
90
Imagine designing a four-bar linkage. You are given all four lengths (a, b, c, d) and the crank angle (theta2). What steps do you take to determine the graphical position snapshot of this linkage?
- Draw the ground link and label O2 and O4.
- Draw L2 (crank) at the given angle.
- Generate an arc from O4 at the given length c; generate an arc from A at the given length b.
- Find the points at which the two arcs meet to resolve the two cases (open and crossed).
How many links are considered for a piston and cylinder? How many joints are considered?
2 links and three full joints.
Which configuration simplifies the kinematic diagram for a piston and cylinder?
a link and slider joint.
A kinematic chain is possible in which Grashof class(s)?
Class 1 and Class 3
List two Greubler Contradictions
- E-Quintet ~ can have 0 or 1 DoF
2. 2 rolling cylinders have 0 DoF
What are the 6 DoF considered for a typical object in space.
X,Y,Z,Roll,Pitch,Yaw
3 translation
3 rotation
What is the maximum mechanical advantage for a fourbar rock crusher linkage? When does it occur?
Infinity ~ it occurs when sin(nu) is 0
What can be said about the motion about an instant center line for two links?
At all points along the line, the point is in pure rotation.
When generating a dynamic model to simulate a real body, what three requirements must be met to have an equivalent model?
- The mass of the model must equal to that of the original body.
- Center of gravity must be in the same location.
- The mass moment of inertia must be equal to that of the original body.
Radius of gyration:
The radius at which the entire mass of the body could be concentrated such that the resulting model will have the same moment of inertia.
Center of percussion:
Point at which no reaction due to impact.
Point of the body in which when struck by a force, will have associated with it another point called the center of rotation at which there will be zero reaction force.
Two force member:
Two forces are equal in magnitude and on the same vector line (opposite in direction).
Three-force member:
The lines of action of the three forces will join at a common point (or points). So long as the forces are coplanar and are not parallel.
When does wmax occur in a flywheel?
After the max negative energy is returned from the load
When does wmin occur in a flywheel?
After the max positive energy is returned from the load
