Leg Rest Extension Analysis

Measurements (in inches) were taken of the linkages where possible. Multi-point ternary and quartenary linkages were divided into triangles and sent through a function to determine the internal angles. With these values, the grounded structure and several linkages were built up using triangulation, using cosine equations for SSS and SAS situations. Several dimensions were left to be calculated in case of measurement error, allowing for small adjustments to be made in the interest of usable linkage equations later on. 

The leg extension moves with three 4 bar linkages, sharing multi-point linkages with offset angled components. L2 is the input driving link with L4 and L9 intermediates. The offset angle L4 is then the driver for the second 4 bar linkage loop with L9 as the output driven link which in turn drives the last set with the target output of L6. The position and angle of L6 represents the leg rest of the recliner after extension in relation to the grounded horizontal (bottom of seat of chair).

The position analysis was plotted as an animation as seen below in Vid. 3, showing the angle range of L6 between closed and fully extended.

Fig. 2 Linkages of Leg Rest Extension

Vid. 3 Leg Rest Extension Range of Motion

Fig. 3 Angle of Link 6 vs Link 2

As a side note, a velocity analysis was also conducted with an arbitrary input speed for L2 to determine the angular velocities of the links in the 4 bar system. Chosen value, w2=1.5708 rad/s. Figure 4 show the velocity ratio of L6 to L2, noting the change in rotation direction.

Fig. 4 Velocity Ratio of L6/L2

Velocity ratio w6/w2 at close= -0.0689

Velocity ratio w6/w2 at extension= -0.1350