Loci - Revision history

DT Online: Added main image

2017-03-14T09:27:13Z

Added main image

← Older revision		Revision as of 09:27, 14 March 2017
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			[[File:Trammel of Archimedes with three sliders.gif\|200px\|right\|Trammel of Archimedes with three sliders\|link=https://en.wikipedia.org/wiki/Trammel_of_Archimedes]]
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DT Online: Added links

2017-03-14T09:15:11Z

Added links

← Older revision		Revision as of 09:15, 14 March 2017
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	More practically it is sometimes necessary to know the path traced by the ends of pieces of machinery to check clearances, estimate the velocities at different parts of a linkage ''(perhaps to calculate ~~momentum~~)'' or to design guarding for example. The general method is to draw the linkage or mechanism in several ‘freeze frame’ positions then draw a smooth curve through the plotted points.		More practically it is sometimes necessary to know the path traced by the ends of pieces of machinery to check clearances, estimate the velocities at different parts of a linkage ''(perhaps to calculate [https://en.wikipedia.org/wiki/Momentum '''Momentum'''])'' or to design guarding for example. The general method is to draw the linkage or mechanism in several ‘freeze frame’ positions then draw a smooth curve through the plotted points.


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	{\| cellpadding="5"		{\| cellpadding="5"
	\|-		\|-
	\| '''Plotting Loci on a Crank and Slider Mechanism'''		\| '''Plotting Loci on a [[Crank and Slider]] Mechanism'''
	\| <span style="color:#B00000">		\| <span style="color:#B00000">
	* Draw a schematic of the ~~crank~~ and ~~slider~~ and divide the ~~crank~~ rotation into a number of equal divisions ''(say, 12)''		* Draw a schematic of the '''[[Crank and Slider]]''' and divide the [https://en.wikipedia.org/wiki/Crank_(mechanism) '''Crank'''] rotation into a number of equal divisions ''(say, 12)''
	* Number the ~~crank~~ positions and, with radius set to the length of the connecting rod, strike arcs from each position along the horizontal line which the ~~piston~~ is constrained to slide along.		* Number the [https://en.wikipedia.org/wiki/Crank_(mechanism) '''Crank'''] positions and, with radius set to the length of the connecting rod, strike arcs from each position along the horizontal line which the [https://en.wikipedia.org/wiki/Piston '''Piston'''] is constrained to slide along.
	* If the requirement is for the ~~locus~~ of the centre of the ~~connecting rod~~, then mark these points on each position and join with a smooth curve as shown.		* If the requirement is for the '''Locus''' of the centre of the [https://en.wikipedia.org/wiki/Connecting_rod '''Connecting Rod'''], then mark these points on each position and join with a smooth curve as shown.
	* It may sometimes be necessary to draw in additional details of the mechanisms, to test clearances for example.		* It may sometimes be necessary to draw in additional details of the mechanisms, to test clearances for example.
	* Loci on parts of other mechanisms can be plotted using a similar process - i.e. draw the mechanism in different positions and connect plotted points to create the ~~locus~~.		* '''Loci''' on parts of other mechanisms can be plotted using a similar process ''(i.e. draw the mechanism in different positions and connect plotted points to create the '''Locus''')''.
	</span>		</span>
	\| [[File:LociCrankSlider.png \|350px\|right]]		\| [[File:LociCrankSlider.png \|350px\|right]]

DT Online at 08:54, 14 March 2017

2017-03-14T08:54:59Z

← Older revision		Revision as of 08:54, 14 March 2017
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	For example: the locus of all points a set distance from another point is a circle; the locus of all points ~~equi-distant~~ from the ends of a line is the [[Basic Constructions\|perpendicular bisector]] of the line; and the locus of all points a set distance from a given line are lines parallel to it ''(or an oval if the locus continues round the ends of the line)''		For example: the locus of all points a set distance from another point is a circle; the locus of all points equidistant from the ends of a line is the [[Basic Constructions\|perpendicular bisector]] of the line; and the locus of all points a set distance from a given line are lines parallel to it ''(or an oval if the locus continues round the ends of the line)''


	More practically it sometimes necessary to know the path traced by the ends of pieces of machinery to check clearances, estimate the velocities at different parts of a linkage ''(perhaps to calculate momentum)'' or to design guarding for example. The general method is to draw the linkage or mechanism in several ‘freeze frame’ positions then draw a smooth curve through the plotted points.		More practically it is sometimes necessary to know the path traced by the ends of pieces of machinery to check clearances, estimate the velocities at different parts of a linkage ''(perhaps to calculate momentum)'' or to design guarding for example. The general method is to draw the linkage or mechanism in several ‘freeze frame’ positions then draw a smooth curve through the plotted points.


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	* Number the crank positions and, with radius set to the length of the connecting rod, strike arcs from each position along the horizontal line which the piston is constrained to slide along.		* Number the crank positions and, with radius set to the length of the connecting rod, strike arcs from each position along the horizontal line which the piston is constrained to slide along.
	* If the requirement is for the locus of the centre of the connecting rod, then mark these points on each position and join with a smooth curve as shown.		* If the requirement is for the locus of the centre of the connecting rod, then mark these points on each position and join with a smooth curve as shown.
	* It may sometimes be ~~neccessary~~ to draw in additional details of the mechanisms, to test clearances for example.		* It may sometimes be necessary to draw in additional details of the mechanisms, to test clearances for example.
	* Loci on parts of other mechanisms can be plotted using a similar process - i.e. draw the mechanism in different positions and connect plotted points to create the locus.		* Loci on parts of other mechanisms can be plotted using a similar process - i.e. draw the mechanism in different positions and connect plotted points to create the locus.
	</span>		</span>

DT Online: Added Template

2016-06-02T19:08:55Z

Added Template

← Older revision		Revision as of 19:08, 2 June 2016
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			=====Description=====

	The [https://en.wikipedia.org/wiki/Locus_%28mathematics%29 '''Locus of a Point'''] is the path traced by a point as it moves in accordance with set conditions and constraints. The plural of [http://www.mathopenref.com/locus.html '''Locus'''] is '''Loci'''.		The [https://en.wikipedia.org/wiki/Locus_%28mathematics%29 '''Locus of a Point'''] is the path traced by a point as it moves in accordance with set conditions and constraints. The plural of [http://www.mathopenref.com/locus.html '''Locus'''] is '''Loci'''.

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	More practically it sometimes necessary to know the path traced by the ends of pieces of machinery to check clearances, estimate the velocities at different parts of a linkage ''(perhaps to calculate momentum)'' or to design guarding for example. The general method is to draw the linkage or mechanism in several ‘freeze frame’ positions then draw a smooth curve through the plotted points.		More practically it sometimes necessary to know the path traced by the ends of pieces of machinery to check clearances, estimate the velocities at different parts of a linkage ''(perhaps to calculate momentum)'' or to design guarding for example. The general method is to draw the linkage or mechanism in several ‘freeze frame’ positions then draw a smooth curve through the plotted points.


			=====Constructions=====

	{\| cellpadding="5"		{\| cellpadding="5"
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	\|}		\|}

			{{Drawing Instruments Buyers Guide}}

DT Online: Completed Loci

2015-02-26T19:40:52Z

Completed Loci

← Older revision		Revision as of 19:40, 26 February 2015
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	The [https://en.wikipedia.org/wiki/Locus_%28mathematics%29 '''Locus of a Point'''] is the path traced by a point as it moves in accordance with set conditions and constraints.		The [https://en.wikipedia.org/wiki/Locus_%28mathematics%29 '''Locus of a Point'''] is the path traced by a point as it moves in accordance with set conditions and constraints. The plural of [http://www.mathopenref.com/locus.html '''Locus'''] is '''Loci'''.

	For example: the locus of all points a set distance from another point is a circle; the locus of all points equi-distant from the ends of a line is the perpendicular bisetor of the line and the locus of all points a set distance from a given are lines parallel to it ''(or an oval if the locus continues round the ends of the line)''

	More practically it sometimes necessary to know the path traced by the ends of pieces of machinery ~~for example - i.e.~~ to check clearances, estimate ~~speeds of~~ different parts of a ~~lunkage~~ or design ~~guards~~		For example: the locus of all points a set distance from another point is a circle; the locus of all points equi-distant from the ends of a line is the [[Basic Constructions\|perpendicular bisector]] of the line; and the locus of all points a set distance from a given line are lines parallel to it ''(or an oval if the locus continues round the ends of the line)''


			More practically it sometimes necessary to know the path traced by the ends of pieces of machinery to check clearances, estimate the velocities at different parts of a linkage ''(perhaps to calculate momentum)'' or to design guarding for example. The general method is to draw the linkage or mechanism in several ‘freeze frame’ positions then draw a smooth curve through the plotted points.


	{\| cellpadding="5"		{\| cellpadding="5"
	\|-		\|-
	\| '''~~###~~'''		\| '''Plotting Loci on a Crank and Slider Mechanism'''
	\| <span style="color:#B00000">		\| <span style="color:#B00000">
	* ~~###~~ </span>		* Draw a schematic of the crank and slider and divide the crank rotation into a number of equal divisions ''(say, 12)''
	\| [[File:~~###~~\|350px\|right]]		* Number the crank positions and, with radius set to the length of the connecting rod, strike arcs from each position along the horizontal line which the piston is constrained to slide along.
			* If the requirement is for the locus of the centre of the connecting rod, then mark these points on each position and join with a smooth curve as shown.
			* It may sometimes be neccessary to draw in additional details of the mechanisms, to test clearances for example.
			* Loci on parts of other mechanisms can be plotted using a similar process - i.e. draw the mechanism in different positions and connect plotted points to create the locus.
			</span>
			\| [[File:LociCrankSlider.png \|350px\|right]]


			[[File:LociPistonCrank2.png\|350px\|right]]
	\|}		\|}
	~~----~~
	~~<span style="color~~: ~~green">'''Note~~:~~'''~~
	~~###~~
	~~</span>~~		[[Category:Secondary]]
	~~----~~		[[Category:Geometry]]
			[[Category:Mechanisms]]

DT Online: Created Loci

2015-02-26T18:41:39Z

Created Loci

New page

The [https://en.wikipedia.org/wiki/Locus_%28mathematics%29 '''Locus of a Point'''] is the path traced by a point as it moves in accordance with set conditions and constraints.

For example: the locus of all points a set distance from another point is a circle; the locus of all points equi-distant from the ends of a line is the perpendicular bisetor of the line and the locus of all points a set distance from a given are lines parallel to it ''(or an oval if the locus continues round the ends of the line)''

More practically it sometimes necessary to know the path traced by the ends of pieces of machinery for example - i.e. to check clearances, estimate speeds of different parts of a lunkage or design guards

{| cellpadding="5"
|-
| '''###'''
| <span style="color:#B00000">
* ### </span>
| [[File:###|350px|right]]
|}
----
<span style="color: green">'''Note:'''
###
</span>
----