PM - Kinematic and Motion Analysis

Motion Synthesis

Our robot can be thought of as two separate but connected 4-bar linkage mechanisms, which is what the basis of the following kinematic analysis is based on. Both 4-bar mechanisms are shown and labeled as such in the following 2 images. The first image has the input motion coming from link 2 (green), which is driven by the motor. There is an angle offset (except when theta2 = 0 deg) that is accounted for with a local XY coordinate system. This coordinate system is always changing throughout the entire motion of the robot because O₂ is stationary, while O₄ is in motion. The conventions follow the same ones used in class and the textbook for this course, such as CCW being the positive angular direction.

The output motion of the bevel gear (link 4) from the above image is directly connected to the input motion of the gripper's gear (link 2) by connection with the gripper's bevel gear, which is then rigidly attached to the right finger's gear. This gear works with the left finger gear, and both fingers were designed to have symmetric motion.

Position Analysis

X: Gripper gear angle

These plots describe the position of the gripper vs. the gripper's gear angle, and ultimately the distance between the two fingers throughout the entire motion.

X: Input motor angle with respect to global frame of reference

These plots relate the input motor angle all the way through the entire mechanism and give the output gripper position, as well as gripper opening width. Also includes a plot relating the global input motor angle to the output bevel gear global angle for the first four-bar mechanism shown in the first image.

X: Link 2 local angle

These plots describe the first four-bar mechanism position shown in the first image with respect to its own local coordinate frame.

Gripper finger 2D and 3D motion. Plots the position of point B for both the left and right grippers. The fingers' motion are symmetric to one another, as expected. The positive Z axis points upwards, towards the ceiling.

Velocity Analysis

X: Link 2 local angle

These plots describe the velocity of links 3 and 4 of the first four-bar mechanism shown in the first image with respect to its own local coordinate frame.

X: Input motor angle with respect to global frame of reference

These plots give the first four-bar mechanism angular velocities with respect to the global input motor angle, as well as relating the input motor angle all the way through the entire mechanism and gives the output gripper velocities.

Acceleration Analysis

X: Link 2 local angle

These plots describe the acceleration of links 3 and 4 of the first four-bar mechanism shown in the first image with respect to its own local coordinate frame.

X: Input motor angle with respect to global frame of reference

These plots give the first four-bar mechanism angular accelerations with respect to the global input motor angle, as well as relating the input motor angle all the way through the entire mechanism and gives the output gripper accelerations.