Qestion-1: An elliptical trammel is a double slider-crank mechanism used for drawing ellipses as shown in figure (a) helow. Position vectors for various linkages are drawn as shown in figure (h). Where: R2: represents position vector for a Slider which can slide along x-axis only R4: represents position vector for a Slider which can slide along y-axis only R3 represents position vector for a crank (Take R3 = 10mm, 03 = 45°, V3 = 10mm/sec) Rix: This is aligned with x-axis and represents fixed position of slider (R4) from ground RIY: This is aligned with Y-axis and represents fixed position of slider (R2) from ground Take: R1x= 20mm, R¡y=40mm. Assume crank is rotating with constant velocity Note: all angles are measured counterclockwise from x-axis. a) Formulate the vector loop, position, velocity and acceleration equations b) Simplify the equations by plugging in respective angles and solve to find R2, R4, linear velocities of both sliders and angular acceleration of crank. c) Identify if the elliptical trammel mechanism can be declared as spatial or planar mechanism also identify if both sliders are moving with same speed. Slider Crank Slotted plate R Slider R Figure (b): Position Vectors Figure (a): Elliptical trammel
Qestion-1: An elliptical trammel is a double slider-crank mechanism used for drawing ellipses as shown in figure (a) helow. Position vectors for various linkages are drawn as shown in figure (h). Where: R2: represents position vector for a Slider which can slide along x-axis only R4: represents position vector for a Slider which can slide along y-axis only R3 represents position vector for a crank (Take R3 = 10mm, 03 = 45°, V3 = 10mm/sec) Rix: This is aligned with x-axis and represents fixed position of slider (R4) from ground RIY: This is aligned with Y-axis and represents fixed position of slider (R2) from ground Take: R1x= 20mm, R¡y=40mm. Assume crank is rotating with constant velocity Note: all angles are measured counterclockwise from x-axis. a) Formulate the vector loop, position, velocity and acceleration equations b) Simplify the equations by plugging in respective angles and solve to find R2, R4, linear velocities of both sliders and angular acceleration of crank. c) Identify if the elliptical trammel mechanism can be declared as spatial or planar mechanism also identify if both sliders are moving with same speed. Slider Crank Slotted plate R Slider R Figure (b): Position Vectors Figure (a): Elliptical trammel
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Oestion-1: An elliptical trammel is a double slider-crank mechanism used for drawing ellipses as shown
in figure (a) below. Position vectors for various linkages are drawn as shown in figure (b).
Where:
R2: represents position vector for a Slider which can slide along x-axis only
R4: represents position vector for a Slider which can slide along y-axis only
R3 represents position vector for a crank (Take R3 = 10mm, 03 = 45°, V3 = 10mm/sec)
Rix: This is aligned with x-axis and represents fixed position of slider (R4) from ground
RIY: This is aligned with Y-axis and represents fixed position of slider (R2) from ground
Take: R13= 20mm, Rịy=40mm. Assume crank is rotating with constant velocity
Note: all angles are measured counterclockwise from x-axis.
a) Formulate the vector loop, position, velocity and acceleration equations
b) Simplify the equations by plugging in respective angles and solve to find R2, R4, linear velocities
of both sliders and angular acceleration of crank.
c) Identify if the elliptical trammel mechanism can be declared as spatial or planar mechanism also
identify if both sliders are moving with same speed.
Slider
Crank
Slotted
plate
R
Slider
Figure (b): Position Vectors
Figure (a): Elliptical trammel
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