Transcript simmechanics model of a rigid body( compound - Ret

SIMMECHANICS MODEL OF A RIGID
BODY( COMPOUND PENDULUM)
BY GILBERT AMADI
MODEL OF SIMPLE PENDULUM
Pendulum simmechanics results
SIMPLE PENDULUM-SIMMECHANICS
• THE PENDULUM IS A SWINGING STEEL ROD
• THE AMPLITUDE OF THE SWING IS LARGE,
THERFORE, THE MOTION IS PERIODIC BUT
NOT SIMPLE HARMONIC
• THE SCOPE(DISPLAY) WILL SHOW ANGLE AND
ANGULAR VELOCITY AS FUNCTIONS OF TIME
• THE XY GRAPH SHOWS THE ANGLE VERSUS
ANGULAR VELOCITY
PROPERTIES OF THE SIMPLE
PENDULUM BODY
• THE SIMPLE PENDULUM IS A UNIFORM,
CYLINDRICAL STEEL ROD OF LENGTH 1
METER, DIAMETER 2cm
• ONE END OF THE ROD, THE FIXED PIVOT FOR
THE ROD TO SWING, IS LOCATED AT THE
GROUND POINT (3,4,5)
• UNIFORM STEEL WITH DENSITY
7.93GM/CC*3,L=1M, R=1CM, MASS=
pπr*2l=2490gram
SIMPLE PENDULUM-SIMMECHANICS
• THE PENDULUM IS A SWINGING STEEL ROD
• THE AMPLITUDE OF THE SWING IS LARGE,
THERFORE, THE MOTION IS PERIODIC BUT
NOT SIMPLE HARMONIC
• THEE SCOPE(DISPLAY) WILL SHOW ANGLE
AND ANGULAR VELOCITY AS FUNCTIONS OF
TIME
• THE XY GRAPH SHOWS THE ANGLE VERSUS
ANGULAR VELOCITY
SIMMECHANIC MODELS
• GROUND BLOCK AND CONFIGURATION
• EVERY MACHINE MODEL MUST HAVE ONE
GROUND BLOCK.
• GROUND BLOCKS FUNCTION AS IMMOBLE
BODIES.
• THE GROUND BLOCK IS CONFIGURED WITH
(3,4,5) IN THE (X,Y,Z) DIRECTION RELATIVE TO
THE WORLD SYSTEM AT (0,0,0)
BODY BLOCK
• A REAL MACHINE CONSISTS OF ONE OR
MORE RIGID BODIES.
• THE MAIN CHARACTERISTICS OF A BODY
BLOCK ARE:
• -ITS MASS PROPERTIES( THE MASS AND
INERTIA TENSOR
• -ITS POSTION(CENTER OF GRAVITY
&ORIENTATION)
• -ITS ORIENTATION IN SPACE
JOINT BLOCKS
• REPRESENTS THE POSSIBLE DIRECTIONS THE
BODY CAN TAKE CALLED ITS DEGRESS OF
FREEDOM(DOFs)
• A JOINT BLOCK IS ALWAYS CONNECTED TO A
SPECIFIC POINT ON THE BODY ON EITHER SIDE
OF THE JOINT.
• THE PEDULUM IS CONNECTED TO THE
GROUND VIA THE REVOLUTE JOINT BLOCK.
SENSORS
• TO MEASURE THE MOTION OF THE PENDULUM AS IT
SWINGS, ONE OR MORE SCOPES BLOCKS ARE ADDED
TO THE MODEL.
• THE SCOPE DISPLAYS THE ANGLE AND ANGULAR
VELOCITY OF THE PENDULUM AS FUNCTIONS OF
TIME.
• THE OTHER SCOPE IS THE XY GRAPH SHOWS THE
ANGLE VERSUS ANGULAR VELOCITY WITH NO
EXPLICIT TIME AXIS.
• THE TWO VARIABLES TRACE OUT A FIGURE SIMILAR
TO AN ELLIPSE, BECAUSE OF THE CONSERVATION OF
TOTAL ENERGY