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constrain the midpoint of a segment to an axis

Message 1 of 4
381 Views, 3 Replies

constrain the midpoint of a segment to an axis

How can you constrain the midpoint of a segment to an axis or a line?

Message 2 of 4
in reply to: c_alessandrelli

Two connected construction lines that are equal length between the circles, that will give you the midpoint. Then a horizontal constraint from that to the third circle.  

Message 3 of 4

@c_alessandrelli wrote:

How can you constrain the midpoint of a segment to an axis or a line?

First identify the segment by its endpoints 𝐴(𝑥1,𝑦1)A(x1,y1) and 𝐵(𝑥2,𝑦2)B(x2,y2). Calculate the midpoint 𝑀M using the formula 𝑀(𝑥1+𝑥22,𝑦1+𝑦22)M(2x1+x2,2y1+y2). To constrain 𝑀M to the x-axis, set its y-coordinate to zero, giving 𝑀(𝑥1+𝑥22,0)M(2x1+x2,0). To constrain it to the y-axis, set its x-coordinate to zero, giving 𝑀(0,𝑦1+𝑦22)M(0,2y1+y2). For constraining 𝑀M to a line 𝑦=𝑚𝑥+𝑐y=mx+c, ensure 𝑀M satisfies the line equation 𝑦1+𝑦22=𝑚(𝑥1+𝑥22)+𝑐2y1+y2=m(2x1+x2)+c. In CAD software, draw the segment, find the midpoint, and use the constraint tools to lock the midpoint to the desired axis or line. Similarly, in geometric software, you can draw the segment, identify the midpoint, and use tools to constrain the midpoint to the axis or line, ensuring accurate alignment as needed.

Message 4 of 4
in reply to: c_alessandrelli

Using construction geometry, create a vertical line from the center of circle one to a point roughly in the middle of the two circles. Now make another construction line from the endpoint of the first line to the center of the second circle. Select both lines and constrain equal. That's your midpoint. Horizontal constraint from that point to the center of the third circle.

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