Kinematics & Dynamics Exam I

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 m_v

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