Motion

6.5. Motion#

So far we’ve looked at actuators individually, e.g. motors and solenoids, and how they create rotation or linear motion. However most machines use multiple actuators working together to create complex movement.

To design and control these systems, it helps to think about their motion, which is shaped by the constraints of the mechanism and the degrees of freedom (DOF) it has. For more advanced systems, like robot arms, we also use inverse kinematics to calculate how to move each actuator to get the end-effector where it is required.

Note

An end-effector is the part at the tip of a robot or mechanism that does the work such as a gripper, pen, welding torch, or tool.

It’s the thing the whole system is built to move, position, or control.

6.5.1. Constraints#

In mechanical design, a constraint is anything that limits how a part can move. Constraints can be created by joints, rails, bearings, or even the shape of the parts themselves.

For example:

  • A sliding rail allows motion in only one straight direction.

  • A hinge allows rotation around only one axis.

  • A ball bearing allows free rotation but prevents sideways motion.

Constraints are important because they convert the raw output of actuators into useful motion. A motor by itself just spins, but mounting it in a linkage constrains how that spin moves other parts.

When designing a mechanism, you deliberately choose constraints to guide the motion to only what is needed, while eliminating unwanted movement.

6.5.2. Degrees of Freedom (DOF)#

Degrees of freedom describe how many independent ways a part can move.

  • A free-floating object in space has 6 DOF: it can move along X, Y, and Z (translation), and rotate about X, Y, and Z (roll, pitch, yaw).

  • A part mounted on a hinge has just 1 DOF: it can rotate around the hinge axis.

  • A part on a sliding rail has 1 DOF: it can move along the rail.

When you add constraints, you reduce DOF. When you add actuators, you can control some or all of the remaining DOF.

This is why robotic arms often have 4, 5, or 6 actuated joints: each joint adds another degree of freedom the robot can control. The number of DOF determines how flexibly the end-effector can move and what positions and orientations it can reach.

6.5.3. Forward and Inverse Kinematics#

Kinematics is the study of motion without worrying about the forces involved. In robotics, we care about how the positions of joints relate to the position of the end-effector (like the tip of a robot arm or gripper).

There are two main problems:

  • Forward kinematics: If you know all the joint angles or positions, where is the end-effector?

  • Inverse kinematics: If you know where you want the end-effector to be, what joint angles or positions do you need?

For example, if you want the tip of a 2-joint robot arm to touch a point on the table, you must calculate how much to rotate each joint to make the tip reach that point. That calculation is inverse kinematics.

In simple systems (like 2-joint planar arms) you can solve the geometry with trigonometry. More complex arms need matrix maths or numerical solvers, but the principle is the same: find joint positions that achieve the desired motion.