Cold Saw/V1 Design Rationale/Hold System/Base - Revision history

YK at 18:13, 19 June 2012

2012-06-19T18:13:35Z

← Older revision		Revision as of 18:13, 19 June 2012
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	[[Image: ColdSawV1Base.png]]		[[Image: ColdSawV1Base.png]]

			=Calculations=

			*Dimensions of mounting rectangle between base plate and base flat

			http://opensourceecology.org/wiki/Cold_Saw/V1_Design_Rationale/Hold_System/Base/Elevated_Mounting_Calculation

			=Parts=

			*Base Plate

			http://opensourceecology.org/wiki/Cold_Saw/V1_Design_Files/Baseplate

			*Base Flat

			http://opensourceecology.org/wiki/Cold_Saw/V1_Design_Files/Base_Flat

YK: /* Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar */

2012-06-19T18:11:04Z

Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar

← Older revision		Revision as of 18:11, 19 June 2012
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	[[Image: ColdSawV1Base.png]]		[[Image: ColdSawV1Base.png]]

	~~=Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar=~~

	~~We want the dimensions to enable the Cold Saw to swivel at least 90 degrees.~~

	~~Assume that what rotates on the swivel hole will be a swivel plate, and that the swivel plate will be long towards the back of the Cold Saw.~~

	~~Assume that the swivel plate's hole is centered along its width.~~

	We are concerned about the width of that swivel plate because it is the swivel plate's width that determines the angle at which the swivel plate contacts the spacers (the ones that isolate the base plate from the base flat bar).

	~~Assume that the spacer is round.~~

	~~Let the length and width from the swivel hole to the spacer hole of the mounting rectangle be '''X''' and '''Y''', respectively.~~

	~~Let the width of the swivel plate be '''W'''.~~

	~~Let the radius of the spacer be '''R'''.~~

	~~Let the swivel angle be '''A'''.~~

	~~Let '''Angle B''', '''Length C''', '''Length D''', '''Angle E''' be placeholder variables that we use only for the calculation but do not include in the final equation.~~

	~~[[Image: ColdSawSwivelAngle.png]]~~

	~~We are solving for '''A'''.~~

	~~From trigonometry, we know that '''cosine of an angle in a right triangle''' equals '''horizontal length''' divided by '''hypotenuse length.'''~~

	*'''1''' So we know that the '''cos(A/2) = (W/2) / (X - Length C)'''

	~~But we don't want '''Length C''' in our solution so let's put it in terms of the desired variables.~~

	~~From trigonometry, we know that '''the length divided by the sine of its associated angle''' equals '''another length divided by the sine of its associated angle'''.~~

	*'''2''' So we know that '''(Length C/sine[Angle B]) = ([Y + Length D]/sine[Angle E])'''.

	~~We see that in the process of solving for '''Length C''', we've introduced 3 more placeholder variables, '''Length D''', '''Angle B''' and '''Angle E'''.~~

	~~Let's quickly solve for these new variables in terms of what we want.~~

	~~From trigonometry, we know that '''the sum of a triangle's inner angles''' is '''180 degrees''', equivalent to about '''3.14 radians'''.~~

	~~So we know after a bit of angle calculations that '''Angle B = (A/2)''' and '''Angle E = 90deg - (A/2)'''.~~

	~~From trigonometry, we know that '''the hypotenuse length of a right triangle''' is equal to '''the vertical length divided by the sine of its associated angle'''.~~

	~~So we know that '''Length D = R / sine[Angle B]'''.~~

	~~Filling in 3 placeholder values in '''2''', we get '''(Length C/sine[A/2]) = ([Y + [R/sine[A/2]] / sine[90deg - A/2])'''~~

	*'''3''' Simplifying, we get '''Length C = (Y(sin[A/2]) + R) / (cos[A/2])'''.

	~~Replacing '''Length C''' in '''1''' with '''3''', we get '''cos[A/2] = (W/2) / ( X - (Y(sin[A/2]) + R) / (cos[A/2]) )'''~~

	~~Simplifying, we get '''Xcos(A/2) - Ysin(A/2) - R - W/2 = 0'''~~

YK at 00:24, 13 June 2012

2012-06-13T00:24:53Z

← Older revision		Revision as of 00:24, 13 June 2012
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			=Notes=

			*The Base Flat mounting holes should be counterbored so that the fastener heads do not interfere with the parallel top surface in case large irregular workpieces need to be mounted to the Base Flat without the Vise.

	=Functions=		=Functions=

YK: /* Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar */

2012-06-12T22:44:52Z

Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar

← Older revision		Revision as of 22:44, 12 June 2012
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	Replacing '''Length C''' in '''1''' with '''3''', we get '''cos[A/2] = (W/2) / ( X - (Y(sin[A/2]) + R) / (cos[A/2]) )'''		Replacing '''Length C''' in '''1''' with '''3''', we get '''cos[A/2] = (W/2) / ( X - (Y(sin[A/2]) + R) / (cos[A/2]) )'''

	Simplifying, we get '''A ~~= 2arccos [ (W~~/2) ~~/ (X~~ - (~~Y(sin[~~A/2]) + R~~) / (cos[A~~/2~~])) ]~~'''		Simplifying, we get '''Xcos(A/2) - Ysin(A/2) - R - W/2 = 0'''

YK: /* Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar */

2012-06-12T22:37:48Z

Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar

← Older revision		Revision as of 22:37, 12 June 2012
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	Replacing '''Length C''' in '''1''' with '''3''', we get '''cos[A/2] = (W/2) / ( X - (Y(sin[A/2]) + R) / (cos[A/2]) )'''		Replacing '''Length C''' in '''1''' with '''3''', we get '''cos[A/2] = (W/2) / ( X - (Y(sin[A/2]) + R) / (cos[A/2]) )'''

	Simplifying, we get '''A = 2arccos(W/2) / ( X - (Y(sin[A/2]) + R) / (cos[A/2]) )'''		Simplifying, we get '''A = 2arccos [ (W/2) / (X - (Y(sin[A/2]) + R) / (cos[A/2])) ]'''

YK: /* Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar */

2012-06-12T22:36:14Z

Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar

← Older revision		Revision as of 22:36, 12 June 2012
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	Assume that the spacer is round.		Assume that the spacer is round.

	Let the length and width of the mounting rectangle be '''X''' and '''Y''', respectively.		Let the length and width from the swivel hole to the spacer hole of the mounting rectangle be '''X''' and '''Y''', respectively.

	Let the width of the swivel plate be '''W'''.		Let the width of the swivel plate be '''W'''.

YK: /* Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar */

2012-06-12T22:15:23Z

Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar

← Older revision		Revision as of 22:15, 12 June 2012
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	*'''3''' Simplifying, we get '''Length C = (Y(sin[A/2]) + R) / (cos[A/2])'''.		*'''3''' Simplifying, we get '''Length C = (Y(sin[A/2]) + R) / (cos[A/2])'''.

	*Replacing '''Length C''' in '''1''' with '''3''', we get '''cos[A/2] = (W/2) / ( X - (Y(sin[A/2]) + R) / (cos[A/2]) )'''		Replacing '''Length C''' in '''1''' with '''3''', we get '''cos[A/2] = (W/2) / ( X - (Y(sin[A/2]) + R) / (cos[A/2]) )'''

			Simplifying, we get '''A = 2arccos(W/2) / ( X - (Y(sin[A/2]) + R) / (cos[A/2]) )'''

YK: /* Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar */

2012-06-12T22:05:49Z

Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar

← Older revision		Revision as of 22:05, 12 June 2012
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	So we know that '''Length D = R / sine[Angle B]'''.		So we know that '''Length D = R / sine[Angle B]'''.

	*'''3''' Filling in 3 placeholder values in '''2''', we get '''(Length C/sine[A/2]) = ([Y + [R/sine[A/2]] / sine[90deg - A/2])'''		Filling in 3 placeholder values in '''2''', we get '''(Length C/sine[A/2]) = ([Y + [R/sine[A/2]] / sine[90deg - A/2])'''

	~~Simplifying~~ '''3''', we get '''Length C = (Y(sin[A/2]) + R) / (cos[A/2])'''.		*'''3''' Simplifying, we get '''Length C = (Y(sin[A/2]) + R) / (cos[A/2])'''.

			*Replacing '''Length C''' in '''1''' with '''3''', we get '''cos[A/2] = (W/2) / ( X - (Y(sin[A/2]) + R) / (cos[A/2]) )'''

YK: /* Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar */

2012-06-12T22:04:00Z

Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar

← Older revision		Revision as of 22:04, 12 June 2012
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	*'''3''' Filling in 3 placeholder values in '''2''', we get '''(Length C/sine[A/2]) = ([Y + [R/sine[A/2]] / sine[90deg - A/2])'''		*'''3''' Filling in 3 placeholder values in '''2''', we get '''(Length C/sine[A/2]) = ([Y + [R/sine[A/2]] / sine[90deg - A/2])'''

	Simplifying '''3''', we get		Simplifying '''3''', we get '''Length C = (Y(sin[A/2]) + R) / (cos[A/2])'''.

YK: /* Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar */

2012-06-12T21:49:27Z

Calculations: Dimensions of the Mounting Rectangle between the Base Plate and the Base Flat Bar

← Older revision		Revision as of 21:49, 12 June 2012
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	So we know that '''Length D = R / sine[Angle B]'''.		So we know that '''Length D = R / sine[Angle B]'''.

	Filling in 3 placeholder values in '''2''', we get '''(Length C/sine[A/2]) = ([Y + [R/sine[A/2]] / sine[90deg - A/2])'''		*'''3''' Filling in 3 placeholder values in '''2''', we get '''(Length C/sine[A/2]) = ([Y + [R/sine[A/2]] / sine[90deg - A/2])'''

			Simplifying '''3''', we get