. .
Understanding the kinematics of a robotic upper arm (Remote Trigger)





 To study the working of an mechanical articulator via remote experimentation. 




Research towards the understanding of motor control need to be studied at a different level of abstraction, for instance, by examining the biochemical mechanisms of neuronal firing, the representational power of single and populations of neurons, neuroanatomical pathways, the biomechanics of the musculoskeletal system, the computational principles of biological feedback control and learning, or the interaction of action and perception.  


Robotic arm are the most useful mechanical devices which are used in the areas where accuracy and precision are needed. These things work similar to human arm and can be programmed as well. Traditional robotic arm will have n number of links, which are connected by n-1 joints with which links are rotate or translate. This links and joints form a Kinetic chain which has an End Effector at the last link.


Terms frequently used while constructing a robotic arm

1) Degree of freedom (DOF)
2) Forward Kinematics
3) Denavit-Hartenberg (DH) Parameters




Arm is an anatomical term also known for upper limb of the human body. Human arm mainly consists of three main parts.


  • The upper arm(Branchium): Between shoulder and elbow
  • The Forearm( Antebranchium): Between elbow and wrist
  • The Hand (Manus)


Human arm consists of mainly 3 bones from shoulder to wrist. They are 


  • Humerus of the upper arm 
  • The radius 
  • The ulna of the forearm.


Besides the bones, arms are also made of muscles, nerves, blood vessels, sinews and veins. Also human arm consists of four joints. They are 


  • The Shoulder joint
  • The elbow joint
  • The wrist joint 
  • The Radioulnar joint


Each joint are different in nature and also possess different degrees of freedom. Movement of human arm is possible in three dimensions depending on the anatomy of the joints. For developing an articulated robotic machine, a detailed study of each joint is essential.


Shoulder Joint: 


Shoulder joints consist of a ball and socket joint. It is also known as glenohumeral joint. The ball in the upper arm is attached to one end which has no perfect round shape. The shoulder joint has the largest range of motion of the joints of the upper limb. The word flexion and extension describes the movement of the upper arm in the Y-Z plane. Flexion is the movement of the arm towards the joint of the body whereas extension is the movement of arm away from the body. The angle of flexion movement is 1650 and that of extension is 650 i.e. a total of 2300.


Elbow Joint


Elbow joint forms the second end of the upper limb. It has a hinge region or joint which allows the possible movement around the axis. The other side of the elbow joint is the forearm. The two bones, radius and ulna in the forearm are connected to the elbow joint. Thus, this joint has two distinct articulations such as Humeroulnar and Humeroradial joints. The movement of elbow joints occurs in Y-Z plane .The angle of movement (i.e. flexion and extension) is varies in male and female. Female shows a total range of movement of 1600 in which 1500 for flexion and 10 for extension. About 85 % of females are able to reach an angle of extension normally but males cannot. When elbow is elonged, the angle between upper arm and forearm is 1800.


Wrist Joint


Wrist joint consists of a double row of four small short bones each.The bones which are next to the forearm form the radiocarpel joint. The second row of bones next to the bone of fingers forms the intercarpel joints. The wrist joints allow the movement of hand in 2 planes. They are Y-Z plane and X-Y plane. The movements of hand up and down are extension (up) and flexion (down) which takes place in Y-Z plane. Abduction means the movement of hand away from the body whereas adduction means the movement of hand towards the body. The angle of movement of wrist joints decreases as the age increases. For a younger person, the range of flexion is 750 and extension is 730 and a total of 1480.Also the range of abduction is 200 and adduction is 360 and a total of 560 .The range of movement of hand varies in person to person on the basis of gender and age.


Radioulnar Joint


The radius and ulna bones in the forearm part forms the Radioulnar joint. The radius rotates around the ulna and both bones ends in wrist. The movement of radioulnar joint is possible only in Y-axis. It is because the two bones of forearm are connected to the wrist and elbow joints. The movement of radius and ulna are allowed by other two joints such as superior radioulnar joint (located towards the elbow joint) and inferior radioulnar joint (located towards the wrist joint).The range of movement is 95 in each direction gives a total movement range of 190.The movement of radioulnar joints is explained in terms of supination and pronation. In supination movement the bones cross each other whereas they are parallel to each other in pronation.


Degree Of Freedom (DOF)


Degree of freedom explains the displacement and deformation of a body. It is the number of independent movement that can perform by a human body in 3D space. A human arm has seven degree of freedom. They are;


  • First Degree: Up and down movement of shoulder which is known as pitch.
  • Second Degree: side to side movement of the upper limb which is known as Yaw.
  • Third Degree: Rotating movement of the upper limb known as Roll.
  • Fourth Degree: The movement of elbow in up and down position which is known as elbow pitch.
  • Fifth Degree: The movement of wrist in up and down  position known as wrist pitch
  • Sixth Degree: The movements of wrist in side to side position known as wrist yaw.
  • Seventh Degree: The movement of wrist in a rotating position known to be wrist roll.




Robots which posses rotating joints are called articulated robots. It always resembles human arm motions. It consists of at least two revolve joints acting around parallel axis. That is, it has two straight links corresponding to the human forearm and upper arm with two joints corresponding to elbow and shoulder joints. The two links are mounted on a rotator table corresponding to the human waist joint. The bodies of articulated robots are made up of partial cylinders and spheres. There are two basic types of articulated robots: vertical and horizontal. Sometimes articulated robots are also known as anthropomorphic because of its resemblance to the motions of the human arm. Anthropomorphic robots (also known as revolute or joint-arm robot) have all rotator joints and motions similar to a human arm. Articulated robots are widely used for the industrial application.






For student’s laboratory studies, it is important to understand the robotic representation of movement information. This is one such experiment that allows students to understand motion in terms of extractable coordinates. 



Determining the Cartesian space co-ordinates of the end-effector using forward kinematics


There are two scenarios that emerge in robotics. One is where the angles of joints are known and the other one is where the end effector co-ordinates are known. In the former scenario, the requirement is to determine the end-effector co-ordinates whereas in the latter scenario, the joint angles are determined.


The forward kinematics problem is to determine the position and orientation of the end-effector, given the values for the joint variables of the robot. The joint variables are the angles between the links in the case of revolute or rotational joints.


As described earlier, a robot manipulator is composed of a set of links connected together by various joints. The objective of forward kinematic analysis is to determine the cumulative effect of the entire set of joint variables. Here, we illustrate a set of conventions that provide a systematic procedure for performing this analysis. A robot manipulator with n joints will have n + 1 links, since each joint connects two links. We number the joints from 1 to n, and we number the links from 0 to n, starting from the base. By this convention, joint i connects link i − 1 to link i. We consider the location of joint i to be fixed with respect to link i − 1. When joint i is actuated, link i moves.


To perform the kinematic analysis, we rigidly attach a coordinate frame to each link. In particular, we attach oxyz (i) to link i. This means that, whatever motion the robot executes, the coordinates of each point on link are constant when expressed in the coordinate frame. Furthermore, when joint i is actuated, link I and its attached frame, oxyz (i), experience a resulting motion. The frame oxyz (0), which is attached to the robot base, is referred to as the inertial frame.


The next step is to determine homogenous transformation matrices for each of the joints with respect to the previous joint. Suppose A (i) is the homogeneous transformation matrix that expresses the position and orientation of oxyz (i) with respect to oxyz (i − 1). The matrix A (i) is not constant, but varies as the configuration of the robot changes. However, the assumption that all joints are either revolute means that A (i) is a function of only a single joint variable, namely q(i).


In other words, A(i) = A(i)(q(i))

 Figure 1: A diagrammatic representation of co-ordinate frames attached to each frame 


Now the homogeneous transformation matrix that expresses the position and orientation of oxyz(i) with respect to oxyz(j) is called, by convention, a transformation matrix, and is denoted by T(i).


T(i) w.r.t j= A(i+1)*A(i+2).A(j) if i < j

T(i) w.r.t j = I if i = j

T(i) w.r.t j = [T(i) w.r.t j ]T if i > j


By the manner in which we have rigidly attached the various frames to the corresponding links, it follows that the position of any point on the end-effector, when expressed in frame n, is a constant independent of the configuration of therobot.


Then the position and orientation of the end-effector in the inertial frame are given by:


H = [T(0) w.r.t n] = A(q(1))....A(q(n)).


 Determining the functions A(q(i)), and multiplying them together as needed. However, it is possible to achieve a considerable amount of streamlining and simplification by introducing further conventions, such as the Denavit-Hartenberg representation of a manipulator.


Denavit Hartenberg parameters


It is possible to carry out all of the analysis for forward kinematics using an arbitrary frame attached to each link; it is helpful to be systematic in the choice of these frames. A commonly used convention for selecting frames of reference in robotic applications is the Denavit-Hartenberg, or D-H convention. In this convention, each homogeneous transformation A(i) is represented as a product of four basic transformations



Transformation matrix


Where the four quantities o(i), a(i), d(i),α(i) are parameters associated with link i and joint i. The four parameters o(i), a(i), d(i),α(i) are generally given thenames link length, link twist, link offset, and joint angle, respectively. A complete transformation matrix has been given below.[10]


Where R is the 3 _ 3 sub-matrix describing rotation and T is the 3 _ 1 sub-matrix describing translation


Calculating DH parameters for a given kinematic chain


The calculation of D-H parameters for a robotic manipulator involves the selection of proper axes. The following are the thumb rules for selecting the properaxes:


1. The Z-axis is in the direction of the joint axis
2. The X-axis is parallel to the common normal between the chosen Z axis. If there is no unique common normal (parallel
Z-axes), then d is a free parameter.This occurs in the case of joints with parallel axes of motion.
3. The Y-axis follows from the X and Z-axis by choosing it to be a right-handed coordinate system.

The transformation is then described by the following four parameters are:



  • d: offset along previous to the common normal.
  • o: angle about previous , from old to new.
  • a: length of the common normal. Assuming a revolute joint, this is the radius about previous Z axis.
  • α: angle about common normal, from old Z-axis to new Z-axis.


An example to illustrate


An example representing the axes chosen for each joint.


The D-H parameters for figure 3.9 are represented by:


The D-H parameters for above example


O(1) and O(2) represent the joint angles and a1 and a2 represent the link length.














Cite this Simulator:

..... .....

Copyright @ 2017 Under the NME ICT initiative of MHRD

 Powered by AmritaVirtual Lab Collaborative Platform [ Ver 00.11. ]