Trig formulas in Excel

R

RCH

New Member
Joined
Nov 17, 2009
Messages
19
Not knowing Trig is rough sometimes. Appreciate your help for the following. I will incorperate solution into a function later.

Thanks,

Associated images are http://www.alibre.com/forum/viewtopic.php?f=9&t=10979&p=65310#p65310

<TABLE style="WIDTH: 395pt; BORDER-COLLAPSE: collapse" border=0 cellSpacing=0 cellPadding=0 width=527><COLGROUP><COL style="WIDTH: 26pt; mso-width-source: userset; mso-width-alt: 1280" width=35><COL style="WIDTH: 81pt; mso-width-source: userset; mso-width-alt: 3949" width=108><COL style="WIDTH: 48pt" span=6 width=64><TBODY><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; WIDTH: 26pt; HEIGHT: 15pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20 width=35></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: #dbe5f1; WIDTH: 81pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl74 width=108>A</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>B</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>C</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>D</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>E</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>F</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>G</TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>1</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl65 colSpan=3>Variable (as shown in image 1)</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>2</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>Wall 180Offset</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>1.250</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=5>(Center of wall at 180 degrees - "left" - of origin)</TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>3</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>Wall Dia</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>8.000</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>4</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>InnerCircDia</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>0.500</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>5</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>OuterCirDia</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>0.500</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>6</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>CirSepLth</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>1.000</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=4>(Inner Circle to Outer Circle - ctr to ctr)</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>7</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl66></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>8</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl65 colSpan=4>Continously variable (as shown in image 1)</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>9</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>SweepAngle</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>90.000</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=4>(from origin - as shown in sketch)</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>10</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl66></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>11</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl66></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>12</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl76 colSpan=7>"Inner Line"</TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>13</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=6>a line drawn from the origin, to the tangency of the inner circle to </TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>14</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=5>an inner wall (circle) drawn concentric to Wall 180offset</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>15</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>16</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl71>results</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl72 colSpan=4>(example results from measuring)</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>17</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl70>@90 deg</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl70>@135</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl70>@180</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl70>@235</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>18</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>InnerLineLength</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>3.553</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>4.527</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>5.000</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>4.323</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>19</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>InnerLineAngle</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>88.560</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>134.200</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>180.000</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>235.960</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>20</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>21</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>OuterLineLength</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>4.060</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>5.040</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>5.500</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>4.841</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>22</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>OuterLineAngle</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>90.980</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>135.560</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>180.000</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>234.320</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>23</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>24</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl75 colSpan=5>Rotation of the inner and outer circles is constrained to </TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>25</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl75 colSpan=6>the midpoint of the "Wall 180Offset" and straight line from origin</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>26</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl75 colSpan=4>through midpoints of the smaller circles.</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>27</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>28</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=7>The resulting circles are "traced" by the smaller inner and outer circles inside </TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>29</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl75 colSpan=7>and outside the "Wall 180Offset" - and fluctuate in radius as the angle sweeps </TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>30</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8">around.</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR></TBODY></TABLE>
 
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No, you are right if pivoting was available.

The concentic circles, sweeping angles and small circles are only a "geometric mechanism" to plot a specific shell relative to the point of origin and the 8 inch circle.

If the concentric circles were redrawn each time it would look like thick lines.

When I use all of the plotted results it would create a double wall, slightly oblong feature.

At 0 and at 180 degrees the seperation is greatest - at .500 inch - and progressivly tapered inward, then outward as the angles change. All because there can be not pivot between the two small circles.

A sketch with lines at 90 and 135 can be found added at the bottom here -http://www.alibre.com/forum/viewtopic.php?f=9&t=10979&p=65409#p65409

There are two pair of concentric lines as a result, but those are only for reference to help locate and solve for the tangent lines. (I cannot post images inline by direct reference).

Thanks
 
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Excel Facts

Will the fill handle fill 1, 2, 3?
Yes! Type 1 in a cell. Hold down Ctrl while you drag the fill handle.
If someone can hop in here and lend a hand, I have to care for an 80 year old Mom full time, alone. 10 minutes uninterupted is a long time here, and my software expires soon. Thanks.
 
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Recently someone posted that although he had mastered 10 foreign languages he was having trouble learning to speak Excel VBA.

You tell us that although you speak Excel VBA, you do not speak trigonometry.

The solution to this problem can proceed stepwise.

I will rephrase your problem as I understand it, as you can confirm if this is correct and this may help anyone else who may work on this.
You have one large circle, called here Circle #1.
If the center of this Circle #1 coincides with the anchor point of line that sweeps around the Circle #1, two smaller circles also sweep along with it, one inside (called here InnerSmallCircle) the larger Circle #1, and one outside (called here OuterSmallCircle) the larger Circle #1.
The smaller circles that straddle the circumference of the larger Circle #1 are not snug up against it, but are equidistant, as the centers of the two small circles are a fixed distance apart, and the middle of the line connecting the centers of the small circles stays on the circumference of the large Circle #1, here and in all that follows.
Thus the edge of the OuterSmallCircle (outside the larger Circle #1) closer to the center of the larger Circle #1, and the edge of the InnerSmallCircle further from the center of the larger circle, also trace circles as the line from the center sweeps around, called here Circle #2 (inside larger Circle #1) and Circle #3 (outside larger Circle #1).

The Line #1 from the center of larger Circle #1 to where the edge of InnerSmallCircle meets Circle #2 overlays the Line #2 from the center of larger Circle #1 to where the edge of OuterSmallCircle meets Circle #3, as the angle of the two lines is the same.

If the anchor point of the line that sweeps around the larger Circle #1 shifts along the x axis away from the center of larger Circle #1, then the Line #1 and Line #2 will still be in phase (and overlapping) when the line is at 0 degrees and 180 degrees, but the phase will shift in between these angles.

The line through the center of InnerSmallCircle and OuterSmallCircle is no longer perpendicular to the circumference of larger Circle #1.

Also, the Circle #2 and Circle #3 will turn, it appears, into ellipses.

You ask for the length and angles of Line #1 and Line #2.

Here are the steps for one approach to solving this problem:

1) Set up the equation for larger Circle #1 and embed a small circle on the circumference (with the center on the circumference line). The small circle can rotate independently.

2) If the small circle rotates at the same angular speed as the large one, then the ends of a line from one side of the circle to the other can be considered to be the centers of InnerSmallCircle and OuterSmallCircle.
Adjust the anchor point of the sweeping line around the larger Circle #1 being off center.

3) Calculate the angles and length of Line #1 and Line#2.

#1 above has been done and the Cell Formulas are below.
The formulas in Row 5 are copied down through Row 504.
The Range =Sheet1!$A$4:$B$504 is plotted on a scatter plot with lines connecting the points with no point markers.

Cell C3 has the radius of the larger Circle #1
Cell D3 has the offset of the center of the larger Circle #1 along the x axis
Cell B1 has the number of rotations (revolutions) of the small Circle, 7 here
This should be 1 for your case
Cell B2 allows for adjustment of the phase of the small Circle

This is not the variable phase that you need to set with the parametric parameter that is added in Column F

This turns out to be an interesting problem, because the formulas below are the basis for a computer version of Spirograph (see Wikipedia), which allows colored ink patterns to be put on paper by rotating geared wheels around each other while tracing with a pen.
Vary Cell E1 and Cell F3, for instance 230 in Cell E1 and 2 in Cell F3.

Sheet1

<TABLE style="PADDING-RIGHT: 2pt; PADDING-LEFT: 2pt; FONT-SIZE: 10pt; FONT-FAMILY: Arial,Arial; BACKGROUND-COLOR: #ffffff" cellSpacing=0 cellPadding=0 border=1><COLGROUP><COL style="FONT-WEIGHT: bold; WIDTH: 30px"><COL style="WIDTH: 64px"><COL style="WIDTH: 64px"><COL style="WIDTH: 64px"><COL style="WIDTH: 64px"><COL style="WIDTH: 64px"><COL style="WIDTH: 64px"><COL style="WIDTH: 64px"><COL style="WIDTH: 64px"></COLGROUP><TBODY><TR style="FONT-WEIGHT: bold; FONT-SIZE: 8pt; BACKGROUND-COLOR: #cacaca; TEXT-ALIGN: center"><TD></TD><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double">A</TD><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double">B</TD><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double">C</TD><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double">D</TD><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double">E</TD><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double">F</TD><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double">G</TD><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double">H</TD></TR><TR style="HEIGHT: 17px"><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double; BACKGROUND-COLOR: #cacaca; TEXT-ALIGN: center">1</TD><TD>Revolutions</TD><TD style="TEXT-ALIGN: right">7</TD><TD style="TEXT-ALIGN: right">0.012566</TD><TD>Large Circle</TD><TD></TD><TD style="TEXT-ALIGN: right">0.087965</TD><TD>Small Circle</TD><TD></TD></TR><TR style="HEIGHT: 17px"><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double; BACKGROUND-COLOR: #cacaca; TEXT-ALIGN: center">2</TD><TD>Phase</TD><TD style="TEXT-ALIGN: right">0</TD><TD>r</TD><TD>a</TD><TD>b</TD><TD>r</TD><TD>a</TD><TD>b</TD></TR><TR style="HEIGHT: 17px"><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double; BACKGROUND-COLOR: #cacaca; TEXT-ALIGN: center">3</TD><TD style="TEXT-ALIGN: right">0</TD><TD style="TEXT-ALIGN: right">0</TD><TD style="TEXT-ALIGN: right">4</TD><TD style="TEXT-ALIGN: right">-1.25</TD><TD style="TEXT-ALIGN: right">0</TD><TD style="TEXT-ALIGN: right">0.5</TD><TD style="TEXT-ALIGN: right">0</TD><TD style="TEXT-ALIGN: right">0</TD></TR><TR style="HEIGHT: 17px"><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double; BACKGROUND-COLOR: #cacaca; TEXT-ALIGN: center">4</TD><TD style="TEXT-ALIGN: right">3.166036</TD><TD style="TEXT-ALIGN: right">0.277334</TD><TD style="TEXT-ALIGN: right">0</TD><TD style="TEXT-ALIGN: right">2.75</TD><TD style="TEXT-ALIGN: right">0</TD><TD style="TEXT-ALIGN: right">0.587965</TD><TD style="TEXT-ALIGN: right">0.416036</TD><TD style="TEXT-ALIGN: right">0.277334</TD></TR><TR style="HEIGHT: 17px"><TD style="BORDER-RIGHT: #f0f0f0 3px double; BORDER-TOP: #f0f0f0 3px double; BORDER-LEFT: #f0f0f0 3px double; BORDER-BOTTOM: #f0f0f0 3px double; BACKGROUND-COLOR: #cacaca; TEXT-ALIGN: center">5</TD><TD style="TEXT-ALIGN: right">3.139747</TD><TD style="TEXT-ALIGN: right">0.363075</TD><TD style="TEXT-ALIGN: right">0.012566</TD><TD style="TEXT-ALIGN: right">2.749684</TD><TD style="TEXT-ALIGN: right">0.050264</TD><TD style="TEXT-ALIGN: right">0.675929</TD><TD style="TEXT-ALIGN: right">0.390063</TD><TD style="TEXT-ALIGN: right">0.312811</TD></TR></TBODY></TABLE>
<TABLE style="FONT-SIZE: 10pt; BORDER-LEFT-COLOR: #00ff00; BORDER-BOTTOM-COLOR: #00ff00; COLOR: #000000; BORDER-TOP-STYLE: groove; BORDER-TOP-COLOR: #00ff00; FONT-FAMILY: Arial; BORDER-RIGHT-STYLE: groove; BORDER-LEFT-STYLE: groove; BACKGROUND-COLOR: #fffcf9; BORDER-RIGHT-COLOR: #00ff00; BORDER-BOTTOM-STYLE: groove"><TBODY><TR><TD>Spreadsheet Formulas</TD></TR><TR><TD><TABLE style="FONT-SIZE: 9pt; FONT-FAMILY: Arial" cellSpacing=0 cellPadding=2 border=1><TBODY><TR style="FONT-SIZE: 10pt; BACKGROUND-COLOR: #cacaca"><TD>Cell</TD><TD>Formula</TD></TR><TR><TD>C1</TD><TD>=PI()*2/500</TD></TR><TR><TD>F1</TD><TD>=PI()*2/500*B1</TD></TR><TR><TD>A4</TD><TD>=D4+G4</TD></TR><TR><TD>B4</TD><TD>=E4+H4</TD></TR><TR><TD>D4</TD><TD>=D$3+C$3*COS(C4)</TD></TR><TR><TD>E4</TD><TD>=E$3+C$3*SIN(C4)</TD></TR><TR><TD>F4</TD><TD>=F3+F$1+B$2</TD></TR><TR><TD>G4</TD><TD>=G$3+F$3*COS(F4)</TD></TR><TR><TD>H4</TD><TD>=H$3+F$3*SIN(F4)</TD></TR><TR><TD>A5</TD><TD>=D5+G5</TD></TR><TR><TD>B5</TD><TD>=E5+H5</TD></TR><TR><TD>C5</TD><TD>=C4+C$1</TD></TR><TR><TD>D5</TD><TD>=D$3+C$3*COS(C5)</TD></TR><TR><TD>E5</TD><TD>=E$3+C$3*SIN(C5)</TD></TR><TR><TD>F5</TD><TD>=F4+F$1</TD></TR><TR><TD>G5</TD><TD>=G$3+F$3*COS(F5)</TD></TR><TR><TD>H5</TD><TD>=H$3+F$3*SIN(F5)</TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE>

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