Robot Kinematics in a Nutshell

In the previous posts, you have seen the basics of robotics, different types of robots, how to choose sensors, actuators, and brains for your robots.

In this section, we are going to discuss the structure and the motion of robots. You have seen different categories of robots in the previous posts. We can widely classify the robots as

Different types of Robots

  1. Robotic arm/manipulators: These robots can manipulate the objects in the environment. The different types of robotic arms are industrial robotics arms, cobots, medical robots, etc.
  2. Mobile robots: These robots can move around in the environment. The robot can either move by wheels, legs, propellers, etc.

In the next section, we can see the basic structure and elements in a robotic arm.

Structure of Robot manipulator

The following figure shows the structure of a typical robot manipulator

Structure of robot manipulator

You can see two main parts in the robotic arm are Links and Joints. A robotic arm is a chain of joints and links. So let’ see what is a link and a joint?

Let’s take an example from the human body. The links and joints of a human arm are demonstrated in the image below. The concept can be applied to robots too.

Joints and Links of a human arm

What is a link in a robot?

Here is one definition of a robot link.

“A link is defined as a single part which can be a resistant body or a combination of resistant bodies having inflexible connections and having a relative motion with respect to other parts of the machine.

A link is also known as a kinematic link or element.

A resistant body is one which does not go under deformation while  transmitting the force.”

Reference: Theory of Machines

There are different division of link in robot.

  1. Rigid link: In this type of link, there will not be any deformation while transmitting the motion. For example, the industrial robotic arm is having rigid links, there will not be any deformation while moving the arm.
  2. Flexible link: In this type of link, there will be a partial deformation while transmitting the motion. One of the examples of flexible links is belt drives.
  3. Fluid link: In this type of link, motion is transmitted with the help of fluid pressure. Hydraulic actuators, brakes are an example of a fluid link.

What is a joint in a robot?

Here is the definition of robot joint

“A joint is a connection between two or more links, which allows some motion, or potential motion, between the connected links. Joints are also called Kinematic pair.”

There are different classification of joints. Here is the main classification of joints based on.

  1. Type of contact between links
  2. Type of relative motion
  3. Nature of constraint or Types of closure

Here are some of joints based on above classification.

Different types of joints

What is a Degrees of Freedom (D.O.F)?

The Degree of Freedom (D.O.F) is one of the parameters commonly using to mention the motion capability of a robot. Here is a simple definition of D.O.F.

D.O.F is defined as the way in which a robot or machine can move. The number of degrees of freedom is equal to the total number of independent displacement or aspects of motion.

An object in space has six degrees of freedom.

Translatory motion along X, Y, and Z-axis (3 D.O.F.)
Rotary motion about X, Y, and Z-axis (3 D.O.F)

The rigid body has 6 D.O.F in space but due to the formation of linkage one or more D.O.F is lost due to the presence of constraint on the body. The total number of constraints cannot be zero as the body has to be fixed at someplace to make the linkage possible. Thus the degree of freedom is given by D.O.F=6

The following example shows the D.O.F of a human arm. We can move the arm in 7 D.O.F.

D.O.F of human arm

The shoulder has 3 D.O.F: Shoulder pitch, shoulder roll and should yaw
Elbow has 1 D.O.F: Elbow
The wrist has 3 D.O.F: Wrist pitch, Wrist roll, and Wrist yaw

The following table shows the D.O.F of different types of joints in robots.

S. No.Geometrical Shapes involvedTranslatory motion (Restrain)Rotary
Degree of freedomTotal restraints
(d)Parallel cylinders2224
(h)Edge slider1142
(i)Cylindrical slider1142
(j)Point slider1051
(k)Spherical slider1051
(l)Crossed cylinder1051

What is Kinematics?

You have seen joints, links, D.O.F in the earlier section. These are some of the terms related to the structure of the robot. In this section, you can see the analysis of the motion of the robot.

The Kinematics is a branch of physics and a subdivision of classical mechanics concerned with the geometrically possible motion of a body or system of bodies without consideration of the forces involved.

Within kinematics, one studies position, velocity, acceleration (and even higher-order derivatives of position) w.r.t. time

Encyclopedia Britannica

In order to control and program a robot, you must have a knowledge of the spatial arrangement and the reference to the environment.

What is a Kinematic Chain of robot?

In mechanical engineering, a kinematic chain is an assembly of rigid bodies connected by joints to provide constrained (or desired) motion that is the mathematical model for a mechanical system.

As in the familiar use of the word chain, the rigid bodies, or links, are constrained by their connections to other links


Here is an example of the kinematic chain of serial link robotic arm.

Serial link manipulator

Forward and Inverse Kinematics

Forward kinematics (for a robot arm) takes as input joint angles and calculates the Cartesian position and orientation of the end effector. The end-effector/gripper is a device or tool that connects at the end of a robotic arm.

Forward kinematics (for mobile robot) takes wheel velocities and calculate the position and orientation of the robot.

Inverse kinematics (for a robot arm) takes as input the Cartesian end-effector position and orientation and calculates joint angles.

Inverse kinematics (for a mobile robot) takes the input as goal position of the robot and calculates the wheel velocities in order to reach the goal.

A brief introduction to forward and inverse kinematics

Top 10 resources for learning Kinematics of a robot

  1. Introduction to Robotics: Mechanics and Control (4th Edition) Book (For robotic arm)
  2. Robotics, Vision, and Control book (for the robotic arm and mobile robots)
  3. Advances in Robot Kinematics (for robotic arm)
  4. Handbook of Robotics (for the robotic arm and mobile robot)
  5. Introduction to Autonomous Mobile Robots, 2nd edition Edition
  6. Robotics Course, WS 14/15, U Stuttgart Course material (For robotic arm & mobile robots)
  7. CMU, Mobile Robotics Kinematics notes (for mobile robots)
  8. Dudek and Jenkin, Computational Principles of Mobile Robotics notes (for mobile robots)
  9. Introduction to Robotics, McGraw hill (for robotic arm)
  10. Robot Kinematics Wikipedia (for robotic arm)

Lentin Joseph

View posts by Lentin Joseph
Roboticist | Author of 8 robotics books | TEDx speaker

Leave a Reply