Re: [CAD_CAM_EDM_DRO] degrees of freedom Was: Angle Iron Ways

This is as close as I can get textually...
Traditionally, the hexapod can be 'constructed' thusly: an equilateral
triangle is 'fixed' in a horizontal plane. A second equilateral triangle (of
the same size, usually) is located some distance away, and directly above
the first, in a plane parallel to the first, except that the verticies of
the second triangle are situated 60° (CW or CCW) with respect to the first
triangle. An extensible strut is then placed from a vertex of the fixed
triangle, to the vertex of the second triangle that is 60° clockwise (or
arbitrarily, CCW) offset. An identically extensible strut is placed from
that same vertex on the second triangle to the vertex of the first triangle
that is clockwise from the first strut. Then a third extensible strut is
placed from that vertex of the first triangle to the vertex of the second
triangle, offset by 60°. Continue in the same manner, until you have all 6
struts located. The struts are all assumed to be connected to the respective
triangle vertices via ball joints. If all the struts are constrained from
extending or retracting, the structure is absolutely (mathematically) rigid.
How ever, if any two adjacent struts are allowed to move, the second
triangle will move, but only as much as the extension/retraction allows. I'm
sure that the struts must act in adjacent pairs i.e. two adjacent struts,
four adjacent struts, or all six struts moving at the same time, in
mathematical co-ordination (That co-ordination is known as kinematic)..

RayHex

-----Original Message-----
From: Stephen Wille Padnos <spadnos@...>
To: CAD_CAM_EDM_DRO@yahoogroups.com <CAD_CAM_EDM_DRO@yahoogroups.com>
Date: Sunday, August 20, 2006 7:12 PM
Subject: Re: [CAD_CAM_EDM_DRO] degrees of freedom Was: Angle Iron Ways

>Raymond Heckert wrote:
>
>>Look closer... If you have 'fixed' length struts (I mean really fixed, not
>>extensible or retractible) the platform cannot move. On a hexapod, at

least

>>two adjacent struts must be extensible to have even one degree of freedom.
>>four adjacent extensible struts should allow you 3 degrees of freedom, and
>>all 6 struts movable should give you your 6 degrees of freedom. ...Unless
>>my observations are greatly in error...
>>
>>RayHex
>>
>>
>Hi there.
>
>I think that four struts aren't enough, unless you can control the joint
>angles in addition to the strut length. Consider a chair with ball
>joints at both ends of each leg. If you extend the legs equally, the
>seat could be raised. But, if the legs "twist" then the seat may stay
>at the same height but rotate (and it could rotate in either direction
>as well!).
>
>With a pair of struts at each of 3 points on the platform, you can
>constrain the location of that point to somewhere on a circle (the plane
>of the circle is perpendicular to the line that joins the two strut
>anchor points, and where it intersects that line depends on the strut
>lengths). With only one strut per platform connection point, the strut
>only constrains the point to be on a sphere, which is much less of a
>constraint.
>
>It's hard to discuss these things textually, but hopefully that
>description helped a little :)