Forward and inverse, it is like a function and its inverse. In robotics for example, this normally refers to calculate the relations between end-effectors and joint angles. So for forward kinematics, the joint angles are the inputs, the outputs would be the coordinates of the end-effectors. On the other hand for inverse kinematics, the given inputs are the coordinates of the end-effectors, the outputs to calculate are the joint angles. For a multiple DOF robot, the forward kinematics is quite straightforward. But inverse kinematics could be tricky, for the same end-effectors coordinates, you may not have unique configuration, especially when the system is redundant. So you would have to define which type of configuration you prefer, in order to control the robot to move in a desired path. 

Hope I understand the question correctly, and the answer could help you. 

The answer is already mentioned by two researchers. I just want to highlight. In  serial linkage type robot, Forward and Inverse kinematics are methods to calculate co-ordinate of end-effector and joint angles respectively. They are opposite.

Suppose you know the all the joint angles of a multi-link robot, therefore you can get the final co-ordinate of the endpoint/gripper of the robot by using  Forward  kinematics.

Forward Kinematics =    to get co-ordinate of end effector from given angles of all joints

Inverse Kinematics is opposite to forward kinematics. Sometimes your multi joint robot needs to follow a given path or trajectory. Or to locate a particular co-ordinate in space, you need to know  all joint angles of all links. 

Inverse Kinematics = to get all joints angle from given co-ordinate(s), path  trajectory plan

In reality Inverse kinematics is complex if the number of serial joint increases.  

In forward kinematics, if you know the joint angles and the lengths, then you can compute the position and the orientation of the end effector with respect to the base. You can use DH notation simply to compute the forward kinematic solution for a a given serial manipulator. 

In inverse kinematics what you know is the end effector position. Using the end effector position you can calculate the joint angles and the lengths. Inverse kinematics is more important for controlling a robot. 

You can refer to Introduction of Robotics Mechanics and Control book and the author is John J. Craig to learn more. Robot analysis book of Lung Wen Tsai also contains information on both serial and parallel kinematics.

Hope this will help you.

in forward kinematics, your inputs are joint space (theta1, theta2,...theta n), and your output which you have to calculate it is cartisian space /or a transformation matrix (multiplications of translation and rotation matrices), so in order to solve it you should calculate DH parameters, be careful with kind of joints your robot has (prismatic/revolute).

in an inverse kinematics, you have the reverse, I mean your outputs are joint space, so based on the  transformation matrix (poisitions of links) which is known, you will calculate the parameters (angles and lengths). two main methods you can used it for solving the inverse problem which are Geometric Solution Approach and Algebraic Solution Approach.

In Forward Kinematics, you determine the end effector pose(position and orientation) from a known input angles. The transformation matrix is useful in representing forward kinematics. while inverse kinematics is just the opposite. From a known end effector pose, to a "unknown" input angles and joint variables.

Dear Mahesh

In Forward Kinematics you should to find end-effector pose (3 parameters for Position and 9 parameters for Orientation) based on joint information( revolute and/or prismatic). But in inverse kinematics you should to calculate joint variables based on Pose information. Due to researches, calculate the FK is easier than inverse kinematics. 

If you have any questions, please don't hesitate to contact me.

Forward kinematics is a mapping function from joint space to Cartesian space and inverse kinematics is mapping from Cartesian space to joint.

Dear Mahesh

i think that this file can help you to understand the difference between forward and inverse kinematics easily . 

In forward kinematics our goal is to determine the coordinate of the end effector (and orientation) for given links angles ( and of course lengths); on other hand, in the inverse kinematics we have the coordinate of the end effector (and orientation) and we need to know, what the different angles between links. In other word we know the Cartesian space and we need to know the configuration space, and Vice versa.

The formulation of the forward (direct) kinematic model of a robot manipulator, named also forward geometric problem, gives the position and the orientation (pose) of the end-effector as a function of the actuated joint variables.

For parallel robotic manipulators, the forward kinematic problem is, in general, difficult and there is no unique solution. Therefore, several ways of assembling a parallel manipulator for given joint variables are possible. These configurations are called assembly modes. This model is can be expressed as following:

x = FKM (ζ)

With x stands for the operational coordinates of the end-effector,

And ζ stands for the joints variables, the latter one depends upon the actuated joints of the robotic manipulator, for example a planar robotic manipulator 3-RRR-type, having three degrees of freedom, the actuated joints are the revolute joints fixed, generally, to the fixed base, so the previous equation can be written as following:

(x, y, φ) = FKM (θ1, θ2, θ3)

But for the spatial parallel robotic manipulator 6-UPS (Gough-Stewart robot), having six degrees of freedom, where the prismatic joints are actuated:

(x, y, z, α, β, γ) = FKM (ρ1, ρ2, ρ3, ρ4, ρ5, ρ6)

The inverse kinematic model is the model which enable designer to find the joint variables with respect to given and specific operational coordinates of the end-effector (the transformation from Cartesian space to the joint space):

ζ = IKM (x)

I hope that helps you to understand these essential notions in robotics.

With all my best regards,

Khaled Assad ARROUK

You guys already defined it so comprehensively i just wanted to make it shorter Forward Kinematics is used to compute the position of the end-effector while inverse kinematics computes the joint parameters.

Sometimes a picture helps

Inverse kinematics takes as input the Cartesian end effector position and orientation, and calculates joint angles.

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

Direct kinematics refers to the use of the kinematic equations of a robot to compute the position of the end effector from specified values for the joint parameters.

Inverse kinematics refers the reverse process that computes the joint parameters that achieve a specified position of the end effector.