Exercise: Motion

6.7. Exercise: Motion#

Question 1

Evaluate the constraints in these three everyday objects:

  • A door hinge

  • A desk drawer on runners

  • A bicycle wheel mounted in its frame

For each one, describe:

  • What kind of motion it allows.

  • What kind of motion it prevents.

  • What part of the object creates this constraint.

Solution

Door hinge

  • Allows: rotation around a single axis.

  • Prevents: sideways sliding and vertical movement.

  • Constraint: the hinge pin connecting the door and frame.

Desk drawer on runners

  • Allows: sliding in and out along one straight path.

  • Prevents: rotation, sideways movement, and lifting.

  • Constraint: the metal runners and guide rails.

Bicycle wheel mounted in its frame

  • Allows: rotation around the axle.

  • Prevents: wobbling side-to-side and sliding along the axle.

  • Constraint: the axle clamped tightly into the frame.

Question 2

You want to make a robot gripper that slides open and closed in a straight line.

Answer the following:

  1. What kind of mechanical constraint would you use to guide this motion?

  2. Why would a hinge not work well here?

Solution

  1. I would use a sliding rail or linear guide to constrain the gripper jaws so they move straight in and out.

  2. A hinge would not work well because it would make the jaws move in an arc. This would change the gap at the tips unevenly and could twist the object instead of gripping it cleanly.

Question 3

A robot arm has three rotating joints in a row, like a shoulder, elbow, and wrist.

Answer the following:

  1. How many degrees of freedom does this give the arm?

  2. What could it do that a 1-DOF arm could not?

Solution

  1. It has 3 degrees of freedom because each joint adds one independent rotational movement.

  2. A 3-DOF arm can move its end-effector to different positions within its working area and can also change the angle of the end-effector. For example, it could pick up objects from different locations and rotate them. A 1-DOF arm could only swing back and forth along one path.

Question 4

The UR3e is a small industrial robot arm. Read the provided datasheet and answer the following:

  1. How many degrees of freedom does it have?

  2. Why does it need that many?

Solution

The UR3e has 6 degrees of freedom, with six independently controlled rotating joints. It needs 6 degrees of freedom so it can position its end-effector in 3D space using X, Y, and Z movement, and also rotate it using roll, pitch, and yaw. This allows the robot to reach around obstacles and place parts at the correct angle during tasks such as assembly.

Question 5

In your own words, explain the difference between forward kinematics and inverse kinematics.

Which is easier to calculate, and why?

Solution

Forward kinematics calculates where the end-effector will be when the joint angles are already known.

Inverse kinematics does the opposite: it calculates the joint angles needed to reach a specific end-effector position.

Forward kinematics is usually easier to calculate because it follows the geometry of the arm directly. Inverse kinematics is harder because there may be multiple possible solutions, or no valid solution at all.

Question 6

Suppose you want the tip of a 2-joint robot arm to reach a point on the table.

What information would you need to calculate this using inverse kinematics?

Solution

You would need to know:

  • The lengths of both arm segments.

  • The coordinates of the target point.

  • The location of the arm’s base.

  • The positions and limits of the joints.

With this information, you can use trigonometry to calculate the two joint angles needed to make the tip reach the target.

Question 7

You are building a small drawing robot that moves a pen around on a flat surface.

Answer the following:

  1. How many degrees of freedom would it need?

  2. What joints and constraints could you use to achieve this?

Solution

  1. It would need 2 degrees of freedom: movement along the X and Y axes.

  2. One way to achieve this is with a gantry system using two sliding rails at right angles. One rail moves the pen left and right, while the other moves it forward and backward. The rails constrain the motion so the pen stays flat on the page and can reach any point in the drawing area.