Kinematic Analysis - Linear motion

The first output of the Dynamic Lion mechanism is a linear motion of the Lion. The linear motion of the Lion comes from a 2-disk cam mechanism. A cam is a rotating piece in a mechanical linkage transforming rotary motion into linear motion. For a 1 disk cam, a full linear motion corresponds to a full rotational motion, and a 2-disk cam mechanism let a full linear motion occur with a half rotation of input. As the disks rotates from an input, the first disk moves the Lion upwards, and as it reaches the highest point, it moves downwards due to gravity. After it makes a full revolution, the second disk takes over, and the same process repeats. Therefore, for a one full rotation of a disk, one full transitional rotation of the Lion happens. 

Three kinematic analysis have been performed for linear motion: 1) position 2) velocity 3) acceleration.

1) Position

Position analysis is the most important aspect for linear motion kinematic analysis. The whole system is a harmonic motion, therefore it follows a graph of cosine. As shown in figure (1), for a full revolution (2 rad), two complete period of the movement occurs. The maximum distance it can reach is 1 cm, which is the maximum distance between the disk plate and the roof. The first half (0°< theta <180°) and the second half (180° < theta < 360°) of the graph corresponds to the movement due to the first disk and the second disk, respectively. 

Figure (1): Position Analysis of the Linear Motion

2) Velocity

The velocity of the linear motion of the mechanism shows a complete sine graph. Unlike the position graph, the velocity graph has a range of ±0.0175 cm/s. A reason there is a negative portion of the graph is that after the Lion reaches the maximum height, the disk plate falls down towards the ground due to gravity. 

Figure (2): Velocity Analysis of the Linear Motion

3) Acceleration analysis

The acceleration graph shows a cosine graph. As shown in the values from the graph, the acceleration is very close to zero, meaning the movement is close to a constant velocity. Since the motion of the mechanism is a harmonic motion, the linear motion of the Lion does not accelerate much. 

Figure (3): Acceleration analysis of the Linear Motion