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Conceptual Questions from iClicker & Textbook know how to
Kinematics
Study of motion without regard to forces
Kinetics
Study of forces on systems in motion
Mechanisms
Device that transforms motion to some desirable pattern
How many degrees of freedom does an object have if it is completely unconstrained
6 Degree of Freedom
Parametric Model Assembly Process
Involves placing parts together by constraining or removing degree of freedom
Rotational Motion
The movement of an object around a fixed axis
Linear Motion
The movement of an object in a straight line
Complex Motion
A combination of Rotational and Linear Motion
Form Closed
The geometric form holds the pair together
Force closed
Some external force holds the pair together
Kinematic Chain
An assemblage of links and joints interconnected in a way to provide a controlled output motion in response to a supplied input motion
Gruebler’s Equation
M=3L-2J-3G
M: Mobility (DOF)
L: # of links
J: # of joints
G: # of ground links
The Grashof Condition Equation
S+L <= P+Q
S: Length of shortest link
L: Length of longest link
P+Q: Summation of remaining link lengths
The Grashof condition definition
Determines if the shortest link in a four-bar linkage can rotate fully
R: Grueblers Equation helps define
Degrees of freedom in a mechanism chain (Mobility)
Mems (Micro-electromechanical system)
A miniature machine that has both mechanical and electronic components
R: The Grashof Condition helps define
Rotatability or output wiggle
R: Gruebler’s Equation predicts movement when in reality it can’t really move
Paradox
R: Motors typically use for mobile applications are
DC motor (Direct Current), because they operate efficiently on batteries, provide good torque control, and allow speed regulation
R: Electric motors that typically run at a set frequency based on the supplied signal are
AC Motors (Alternating Current)
Function Generation
Input vs. Output motion
Path Generation
Control of a point along a path (Don’t care about the link orientation)
Motion Generation
Control of a line in a plane (Care about the link orientation)
Stationary Positions
Where a rocker stops and changes directions
Transmission angle
Angle that the linkages form to transmit force (90 degrees is perfect but hard to achieve, below 40 is a waste of time without inertia)
Position Synthesis
To determine the ratios of the linkages to get the job done
R: Making a DC or AC motor rotate by changing the state of the magnetic fields is called
Commutation - The process of switching the direction of current in the motor windings to produce continuous rotation
Cusp
A sharp point on a curve (Means there is instantaneous zero velocity position)
Crunode
A double point where the curve crosses itself
Cognate
When a linkage of different geometry produces the same coupler curve
Roberts-Chebyschev Theorem
Three different planar pin-jointed four-bar linkages will trace identical coupler curves
Hartenbrg and Denavit extensions
Two different planar crank-slider linkages will trace identical coupler curves
Parallel Motion
When a coupler moves without changing orientation
Dwell Mechanism
Zero output motion for some nonzero input motion
R: Coming up with a design no one has ever thought of before is known as
Synthesis - The process of creatively combining elements to develop new designs, solutions, or systems
Global or absolute coordinate system
Something that doesn’t change in the problem (Earth or reference frame)
Local Coordinate System
Can move within a problem
Inertial reference frame
A system which itself has no acceleration
R: The optimum transmission angle is (Degrees)
90
POSE
Position of a point on the link and the orientation of a line on the link
Translation
All points on the body have the same displacement
Curvilinear
Moving in a curve
Euler’s Theorem
The general displacement of a rigid body with one point fixed is a rotation about some axis
Chasles’ Theorem
Any displacement of a rigid body is equivalent to the sum of a translation of any point on that body and a rotation of the body about an axis through that point
R: A stationary position in a linkage motion is a position where the link
Stops & Reverse direction
Vector loop equation for a fourbar linkage
is measured from the root, not the head
R: Position of a point on the link and the orientation of a line on the link is called
POSE
R: Sum of translation and rotation of components is
Complex Motion
R: A system which itself has no acceleration is called
Inertial Reference Frame
R: Positive angles with respect to inertia reference frames are
Anti-clockwise (Counter Clockwise)
R: All points on the body have the same displacement is called
Translation
R: Total Displacement=
Translation component + Rotation component
Transmission Angles
Angle between the output link and the coupler link (*Can be between any two links)
Toggle Positions
when two links in a mechanism become collinear, causing a loss of mobility and extremely high mechanical advantage
Circuit
All possible orientations of the links that can be realized without disconnecting joints
Branch
A continuous series of positions of the mechanism on a circuit into a series of branches
Circuit Defect
When needs to be disassembled to reach a position
Branch Defect
Needs a circuit change to reach a position
Newton-Raphson Solution Method
an iterative numerical technique used to find successively better approximations of the roots (or zeros) of a real-valued function
Position Analysis
Seeing how and where someone else’s linkage design moves
R: Rectilinear is
Moving in a straight line
R: Kinematic theorems involving rotations
Euler’s and Chasles’
Simplified Euler’s Theorem
Every motion of a rigid body about a fixed point is a rotation about an axis through a fixed point
Simplified Chasles’ Theorem
The most general rigid body displacement can be produced by a screw displacement
R: Toggle Positions
Are when a link moves, stops, and reverse direction
R: Circuit
All possible orientations of the links that can be realized without disconnecting joints
Function (Kinematic Synthesis)
Correlation of an input function with an output function in a mechanism
Path (Kinematic Synthesis)
Control of a point in the plane such that it follows some prescribed path
Motion Generation (Kinematic Synthesis)
Control of a line in the plane such that it assumes some sequential set of prescribed positions
Precision Points
Positions on some links that the mechanism must pass
R: Control of a point in the plane such that it follows some prescribed path is
Path synthesis
R: Maximum number of precision points is determined by
Degrees of freedom, Number of independent equations that can be written, number of links
R: Control of a line in the plane such that it assumes some sequential set of prescribed positions
Motion generation synthesis
Ludwig Burmesterr
Developed geometric techniques for synthesis of linkages in the late 19th century
R: Correlation of an input function with an output function in a mechanism
Function synthesis
[A]^-1x[A] for non-zero matrices is
Identity Matrix [I]
R: Positions that the mechanism must pass through are known as
Precision Points
Velocity is the
Rate of change of position with respect to time
Velocity is
Linear or angular, always in a direction perpendicular to the radius of rotation and is tangent to the path of motion
Absolute velocity
Referenced to the global coordinate axis
Relative velocity
The speed of two points in different bodies
Instant centers of velocity
A point, common to two bodies in plane motion, which point has the same instantaneous velocity in each body
Number of Instant Centers =
(1/2)(n(n-1))
n=number of bodies
Kennedy’s Rule
Any three bodies in plane motion will have exactly three instant centers and they will be in the same straight line
Angular Velocity ratio mv
The output angular velocity divided by the input angular velocity
Indices of merit
How we judge different linkages on how they accomplish a task
Compliant linkage
Uses elastic deformations of the links as hinges instead of pin joints
R: Speed of two points in the same body
Velocity Difference
R: Speed of two points in different bodies
Relative Velocity
R: Indicies of merit for a linkage are
Angular velocity Ratio, Mechanical Advantage
IC of a tire while slipping
The whole tire
IC of a tire during burnout
Center of tire
R: The curve created by tracing all the instant centers for a link is known as
Centrode
R: Axis of transmission and axis of slip are
Perpendicular
