Design and Kinematic Analysis

Before design work can begin on the assembly, the angular velocity profile of an ideal pour must be known. A video of a bottle of beer being manually dispensed was recorded and divided into frames every 0.25 seconds. Each frame was then analysed as shown in Fig. 1 to determine the angular position of the bottle with respect to a fixed reference axis. With this data, the angular velocity profile of the beer bottle was plotted (Fig. 2).

Fig. 1: Video analysis of beer pouring

Fig. 2: Recorded angle vs. displacement for poured beer

Having obtained a target angular velocity profile for the bottle, design of the mechanical components of the robot could proceed. The assembly was modeled as a four-bar, crank-rocker linkage driven at a constant angular velocity, with a linear cam attached to the output link. The bottle is in turn driven by an interface between the cam, i.e. the guide arm, and a follower offset from the bottle's pivot point. In order to determine the profile of the guide arm, the geometry of the four-bar linkage and the bottle's pivot position relative to the linkage was decided. These geometry decisions were largely arbitrary, however care was taken to limit the size of the linkage to reduce fabrication time and cost.

In order to limit the bottle's motion to the desired pouring action, the guide arm must be designed to execute this motion between the toggle positions of the four-bar linkage. Once the toggle positions have been analytically determined, the angular position profile of the output link is calculated (Fig. 3).

Fig. 3: Angle of output link between toggle angles

At this point, the position of both the output link and the bottle is known for any given time. By calculating the distance from the output link's pivot and the bottle's cam-follower within a reference frame fixed to the output link, the center of the cam/guide arm for that particular instance in time is known (Fig. 4). Performing this calculation for a large number of instances allows for the generation of spline defining the profile of the cam (Fig. 5).

Fig. 4: Calculation of linear cam profile

Fig. 5: Linear cam profile

The output link was then modified to include a slotted profile matching that defined in Fig. 5. The completed link can be seen in Fig. 6; large thru holes on the left and in the middle of the part allow for revolute attachments to ground and the intermediate crank-rocker link respectively. The arrays of six thru holes surrounding the link connection point provide an appropriate mating surface for universal-mounting-hubs. These hubs rigidly connect the link to an axle. The linear cam joined to the rest of the part via "webbed" material connections.

Fig. 6: Four-bar output link with linear cam