Tangent

Definition

T [-]radius1,[-]radius2,heading,distance[?]

T	tangent command
[-]radius1	Radius of the first circle in working units. A positive value for CW and a negative for CCW
[-]radius2	Radius of the second circle in working units. A positive value for outside tangent and a negative for inside tangent.
heading	Heading in degrees relative to the current heading indicator of the vector connecting the center of the two circles.
distance	Distance between the center of the two circles.
?	Complete the arc to the next quadrant crossing from the tangent point along the arc of the second circle.

Usage

Understanding the heading can be a bit tricky. Remember the heading is the angle formed between initial heading and a line connecting the circle centers.

A 90 degree angle is formed between two imaginary lines. The first extending the initial heading and the second passing through the two circle centers.

t1,2,90,4


In this example a 45 degree angle is formed. The quadrant completion (?) has been set to extend the tangent line around the target arc to the next quadrant boundary.

t1,2,45,4?



There are four combinations of clockwise/counterclockwise and inside/outside as follows:

CW/outside
t1,2,90,4


CW/inside
t1,-2,90,4


CCW/outside
t-1,2,90,4


CCW/inside
t-1,-2,90,4



The same examples with quadrant completion (?) set:

CW/outside
t1,2,90,4?


CW/inside
t1,-2,90,4?


CCW/outside
t-1,2,90,4?


CCW/inside
t-1,-2,90,4?



Example 1

The tangent command is perhaps the most powerful D2nc command. It opens up the possibility of countless shapes not possible before in the previous versions.


r{t.2,.2,90,1}4& r{t.2,.1,90,1}45


In this example, a bracket is formed by two tangent lines on two circles with a box shape below. The bottom circle is 2 inches in diameter and the top 1 inch. The center of the circles are 2 inches apart. The heading of the line connecting the circle centers is on the same heading as the initial heading so they are zero degrees apart. A detailed explanation of the heading can be found in the tangent reference section.

t1,.5,0,2


The shape created is the initial part of the arc to connect to the tangent line and the tangent line itself. This leaves the heading at some value we can get by looking at the Shape detail display which shows 75.52 degrees. We could draw an arc of 75.52 degrees with a radius of .5 (a75.52,.5) or we could just specify the quadrant completion (?) setting of the tangent command. The quadrant completion will extend the tangent line around the second circle until a quadrant boundary is reached.

t1,.5,0,2?


Now we can specify another tangent this time from the small circle to the large. Notice this time the heading will be 90 degrees between the current heading and circle centers. We also need to extend to the next quadrant. The program so far will now look line this:

t1,.5,0,2?
t.5,1,90,2?



The shape can now be finished off with the bottom box shape

t1,.5,0,2?
t.5,1,90,2?
d1,90
d2,90
&


There you have the complete bracket outline ready to define a path and machine.


Example 2

The rocker arm illustrates the use of the tangent command and is a simple shape made up of four tangents. This shape comes from a live project and is the reason behind the creation of the tangent command. While the shape could have been define previously it required some math to calculate the arc angles and line distances. Too much to do in the machine shop and a simple command was needed.

The rocker arm is three circles spaced .67 apart the outer two circle have a radius of .1 and the center circle a radius of .1625. Given those dimensions, the following four tangent commands create the shape.




t.1,.1625,90,.670?
t.1625,.1,0,.670?
t.1,.1625,90,.670?
t.1625,.1,0,.670?

or

r{
t.1,.1625,90,.670?
t.1625,.1,0,.670?
}2