Static balancing involves ensuring that the motors do not contribute towards supporting the mechanism's weight, for any of the possible configurations. A mechanism can therefore remain stable in any position without the help of motors or brakes. This result can be obtained by using counterweights or springs. The most common application of this concept at the present time is that of desk lamps (Figure 1). The balancing of these lamps is possible through the use of springs, but also as a result of friction, which we will not rely on in robotic mechanisms. Static balancing is mainly useful in applications involving heavy loads (for example, flight simulators).

A statically balanced mechanism can be obtained by achieving a potential energy which remains constant irrespective of the position and orientation of the mechanism. The potential energy expression must thus be found, its derivative equalled to zero and the system of equations solved.

Several parallel mechanisms have been studied in the laboratory, including 3-DOF planar mechanims, 2- and 3-DOF spherical mechanisms as well as 4-, 5- and 6-DOF spatial mechanisms. From the theoretical results obtained, a large number of designs were proposed for statically balanced parallel mechanisms and several wooden prototypes were developped. For example:

• A 1-DOF spring-balanced mechanism (Figure 2). This is the simplest example which leads to a clear understanding of the relationships between the masses, the connecting/joint positions, the stiffness of the spring and the sense of gravity.
• A 3-DOF planar mechanism, statically balanced using counterweights and springs (Figure 3). This mechanism is of the type 3-RRR planar. The springs are placed on the base of the mechanism and are connected by a system of pulleys.
• A 3-DOF planar mechanism, statically balanced using springs (Figure 4). A parallepiped was added to the proximal members to achieve the balancing without the use of counterweights.

A robotic prototype was also designed for a spatial 6-DOF mechanism statically balanced using springs (Figure 5). The mobile platform is connected to the base by 3 legs each consisting of a 5-bar mechanism. In the event that this architecture finds interesting applications as a base structure for motion simulators, for example, and more specifically for flight simulators, the use of springs was preferred over the use of counterweights, since the latter substantially increase the total inertia of the structure when large accelerations of the platform are required.

A poster was prepared in 2002 on a 6-DOF spatial statically balanced mechanism. The poster can be downloaded with the following PDF file.

A robotic prototype was also built of a 3-DOF planar mechanism (Figure 8). Five-bar mechanisms in the shape of parallelogram were chosen to build the legs since they allow the balancing conditions to be simplified.

The counterweights serve to maintain a constant position for the centre of mass while the counter-rotations are used to maintain a constant angular moment. The counterweights, the counter-rotations and the effector are made of steel. The mass of the effector is 0.1 kg and that of the mobile parts is about 4 kg.

Several posters were prepared in 2002 on dynamic balancing. The posters can be downloaded with the following PDF files.