Spatial rings and domes 75
4.4 Other design considerations
4.4.1 Corner connectors
At the corners of either a ring or a dome, corner joint pieces are used
where beams from the scissor- like elements in a loop and tie meet. The
upper and lower pieces, together with beams being connected, form a
Sarrus linkage. The derivations for both rings and domes are based on an
implicit assumption that the links and the joints have no physical size. This
is true if the axes of all revolute joints meet at a single point but this is not
always possible.
The derivations in the previous sections can be modified to include the
distances between the axes of end connectors of scissor- like elements and
the point where all the axes are supposed to meet, known as the eccentricities. Take a ring based on concept A as an example. Let Λ and Δ be the
eccentricities of corner joints pieces at outer loop and λ and Δ be those of
pieces at inner loop, see Figure 4.12. The projection lengths given in Eq.
(4.5) need to be modified to reflect them. Now,
,
and
.
(4.27a, b, c)
Substituting the above expressions into Eq. (4.4) gives
, (4.28)
Figure 4.12 Projection of a portion of a ring based on concept A with eccentricities at the corner joint pieces. Arrows represent the axes of the
revolute joints at the ends of scissor-like elements.
4.4 Other design considerations
4.4.1 Corner connectors
At the corners of either a ring or a dome, corner joint pieces are used
where beams from the scissor- like elements in a loop and tie meet. The
upper and lower pieces, together with beams being connected, form a
Sarrus linkage. The derivations for both rings and domes are based on an
implicit assumption that the links and the joints have no physical size. This
is true if the axes of all revolute joints meet at a single point but this is not
always possible.
The derivations in the previous sections can be modified to include the
distances between the axes of end connectors of scissor- like elements and
the point where all the axes are supposed to meet, known as the eccentricities. Take a ring based on concept A as an example. Let Λ and Δ be the
eccentricities of corner joints pieces at outer loop and λ and Δ be those of
pieces at inner loop, see Figure 4.12. The projection lengths given in Eq.
(4.5) need to be modified to reflect them. Now,
,
and
.
(4.27a, b, c)
Substituting the above expressions into Eq. (4.4) gives
, (4.28)
Figure 4.12 Projection of a portion of a ring based on concept A with eccentricities at the corner joint pieces. Arrows represent the axes of the
revolute joints at the ends of scissor-like elements.