Mach Elem Flashcards
particles composing the body are equal and parallel
translation
It is necessary to know the velocity of only one particle in order to find the velocity of any other particle.
Velocities in Machines
It is necessary to have enough data to determine the velocity of two particles in order to determine the velocity of any part of the body.
coplanar
Analyzing velocity of a rigid body, point and particle will be used interchangeably.
- two or more points on the same body
- points on two or more bodies connected by pin joints
- points on bodies in rolling contact
- points on bodies in sliding contact
Velocities and accelerations in machines may be quite complicated, impossible.
Analytical analysis
Velocities and accelerations in machines may be more direct, less complicated, and usually sufficiently accurate.
Graphical analysis
Four commonly used methods for obtaining velocities:
- Resolution and composition
- Instantaneous axis of velocity
- Centro
- Relative velocity or velocity polygon
give the quickest solution methods for obtaining velocities
- Resolution and composition
- Instantaneous axis of velocity
can be used in the solution of practically all problem and the most desirable method
. Relative velocity or velocity polygon
quantity has magnitude only
scalar
has magnitude, direction, and sense
A vector quantity
represents a vector quantity
vector
The sum of the quantities is called
resultant
The sum of the quantities and its vector
resultant vector.
The quantities added together to obtain the resultant are its
components
The quantities added together to obtain the resultant, and the corresponding vectors are the
component vectors.
The process of obtaining the resultant of any number of vectors is called
vector composition
reverse process of breaking up a vector into components is called
vector resolution.
It is necessary to draw the machine full scale, to a smaller scale, or to a larger scale
Scales
It is necessary to draw the machine full scale, to a smaller scale, or to a larger scale, This _______ is expressed in three ways
space scale
space scale is expressed in three ways:
- Proportionate size, eg (¼ scale, 1:2)
- Number of inches on the drawing equal to 1 foot on the machine, eg (3 in. = 1 ft)
- 1 inch on the drawing equals so many feet, eg (1 in. = ⅓ ft, 1 in. = 1/34 ft)
designated Kv, defined as the linear velocity in the distance units per unit of time.
Velocity scale
designated Ka, defined as the linear acceleration in distance units per unit of time per unit of time
Acceleration scale
Magnitude of the instantaneous linear velocity of a point on a revolving body, rotating crank, or oscillating crank is proportional to the distance of that point from the axis of rotation of the body or crank.
Rotating and Oscillating Cranks
If the velocity of one point and the direction of the velocity of any other point on a body are known, the velocity of any other point on that body may be obtained by resolving the known velocity vector into components along and perpendicular to the line joining theses points and making one of the components of the velocity of the other point equal to the component along the line.
Resolution and Composition
Instantaneously this moving axis may be thought of as a stationary axis with properties similar to a fixed axis. In other words, The cranks of a machine rotate or oscillate about their respective fixed axes and
Instantaneous Axis of Velocity
A method for obtaining the instantaneous absolute angular velocity of a floating link.
Angular Velocity of a Floating Link
If a wheel rolls along the surface without slipping the point of contact of the wheel and the surface is the instantaneous axis of velocity and the entire wheel acts as if it were a crank rotating about the axis Q.
Instantaneous Axis of Rolling Bodies
the instantaneous axis of velocity method of obtaining velocities is a simplified version of the _____ method and can be used in obtaining velocities when the instantaneous axis can be located.
Centros
By using the method of _______, velocities in all mechanisms can be obtained.
Centros
A centro may be defined as:
- A point common to two bodies having the same velocity in each
- A point in one body about which another body actually turns
- A point in one body about which another body tends to turn
is also the definition of an instantaneous axis of velocity
A point in one body about which another body tends to turn
All links, including the frame, are numbered as 1, 2, 3, and so on.
A centro has a double number as 12, 13, 24, and so on.
Notation of Centros
The _______ in a mechanism is the number of possible combinations of the links taken two at a time.
Number of Centros
Number of Centros may be obtained by the equation
Number of centros = N(N - 1)/2
Where: N = number of links, including the frame, in the mechanism
Centros are located by:
- Observation
- The application of Kennedy’s theorem
which stated that any three bodies having plane motion relative to each other have only three centros which lie along the same straight line. In other words, the three centros that are akin to each other lie along the same straight line.
Location of Centros
Is used to determine the velocities of different points on links of a mechanism for a given input motion. Determination of the motion characteristics of links in a mechanism is required for the force analysis.
VELOCITY ANALYSIS
Velocities of links and of points of mechanism can be determined by different methods.
Relative velocity method or velocity polygon method
Instantaneous center method.
an imaginary instantaneous point about when a link is assumed to rotate
Instantaneous center
Types of I-centers
Fixed
Permanent
Neither fixed nor permanent
Types of I-centers
remain in same plane for all configurations.
Fixed
Types of I-centers
moves when the mechanism moves
Permanent
Types of I-centers
vary with the configuration of the mechanism.
Neither fixed nor permanent
The method of centros affords an excellent manner for determining the instantaneous angular velocity ratio of any two link and the instantaneous absolute angular velocity of any link when the instantaneous absolute angular velocity of one link in a mechanism
Angular Velocities of Links
All motions, strictly speaking, are relative motion in that some arbitrary set of axes or planes must be established in order that the motion may be defined. It is customary to assume that the earth is a fixed reference plane when analyzing the velocities and motion of machine members, and to refer to such motion as absolute motions.
Relative Velocity
A _______ in a machine, rotating about an axis fixed to the machine frame which is attached to a foundation in the earth has absolute motion
crank
A ______, the connecting rod of a machine, has motion relative to the crank.
floating link
The principles discussed in the preceding article afford a useful method of obtaining the instantaneous angular velocities of the members in a machine and the instantaneous linear velocities of points on these members.
Relative Velocity Method of Obtaining Velocities
