Planar and Spatial Gravity Balancing With Normal Springs

Abstract

Very often, spring-to-gravity-balancing mechanisms are conceived with ideal (zero-free-length l0=0) springs. However, the use of ideal springs in the conception phase tends to lead to more complex mechanisms because the ideal spring functionality has to be approximated with normal springs. To facilitate construction of (gravity) balancers, employing normal springs (l0≠0) directly mounted between the link attachment points of the mechanism in the conception phase therefore seems beneficiary. This paper discusses spring mechanisms that enable perfect balancing of gravity acting on an inverted pendulum while employing normal springs between the spring-attachment points: The design synthesis of such mechanisms will be explained and balancing conditions will be derived, using a potential energy consideration.

Static balancing of an inverted pendulum with prestressed torsion bars

“…In addition, most spring-based balancing techniques rely on the use of a special type of spring, namely a zero-free-length spring (ZFLS), which is not a common off-the-shelf component. Some authors have presented ways to circumvent the need for ZFLS proposing alternative balancing methods that are based on conventional springs with non-zero free-length [16,17,18,19,11].…”

Spatial Static Gravity Balancing With Ideal Springs

“…As is also the case for planar static balancing spring-to-spring mechanisms [1][2][3][4][8][9][10][11], it is seen that the conditions for the three-spring balancer shown in Fig. 3 (eq.…”

“…It should be noted however that the gravity or 'extra spring' balancing mechanisms discussed in this paper do not allow for normal spring application in such a manner. Bearing in mind the constructional difficulties of ideal spring application, further research focused on the static balancing of gravity acting on inverted pendulums with both hinge [10,11] and spherical joints [11] by means of normal springs mounted directly between their attachment points.…”

“…It is noteworthy that after adding 'extra masses' -or 'extra springs' to the basic three-spring mechanism (to re-establish perfect balance), the resulting mechanism does not allow for shifting apart or overlapping the apexes of the cones with a distance l sh anymore (through employing technical springs with a free-length l 0 =l sh ). After all, the added masses or springs then no longer rotate through an angle θ about one pivot but about two pivots with two links such that the rotation of θ of one link causes an additional rotation of θ/2 of the other link (see also the companion paper [11]). Thus the conditions set out in eq.…”

“…However, although achieving ideal spring functionality with normal springs is possible it tends to complicate mechanism construction, especially with large spring pre-stresses in combination with relative large mechanism movements. Solutions employing normal springs are addressed in a companion paper [11].…”