There is a lot of engineering that goes into devices and gadgets. Systems where motion is involved especially need special attention. Cars, aero-planes, locomotives, robotics, etc. all involve motion. And this motion is complex because many of the bodies are attached to each other and are required to move as a complete system. Take for example an automobile. The moving parts of an automobile comprise of the differential that transmits an engine’s torque to the wheels. The wheels themselves can move at different speed, especially at the turns. Likewise, there are other complex industrial systems that require various parts (which are linked together in some way), to move in unison. Such systems are called multi-body systems, and their motion analysis is one of the most important aspects of designing them. Since the loads vary, their modelling requires kinematic loops and differential equations.
What is Kinematics?
Study of motion has been an integral part of Physics. Where will a football land when it is thrown at a certain angle? What will happen to a missile fired at an angle of 45 rather than 50 degrees? How do the various planets move? All these are questions that involve motion. There are two main branches of Mechanics that studies motion - Kinetics and Kinematics. In this article, we will talk about kinematics and their relation with multi-body dynamics. Before we talk about kinematics, let us first understand the difference between kinematics and kinetics.
Kinematics is the branch of Mechanics that is concerned with the motion of entities, without taking cognizance of the cause of the motion. In other words, kinematics studies motion without regard to why it is occurring. It differs with kinetics in this respect; kinetics is concerned with studying the underlying cause of the motion as well. That is, kinetics studies the underlying force that makes the objects or systems move. Kinematics involves only the geometry of the motion and is not concerned with the underlying laws (Newton's or Euler's) of motion. Kinematics is therefore also called as the 'geometry of motion'. Coming back to the question of the football, kinetics is concerned with the force with which the ball has been kicked, while kinematics is only concerned with the trajectory of the football after it has been airborne.
What is Dynamics?
Dynamics is the science that describes the motion of bodies. Mathematically speaking, Dynamics is the branch of Physics that determines the position and velocity of an object under the action of forces. Dynamics is used to finding a set of differential equations that describes the trajectory of a body in motion. A trajectory of an object signifies the complete specification of the three positions and three speeds of a point in a reference frame as a function of time. Before the advent of powerful computers, solving equations of motion was an extremely tedious task. However, the numerical analysis of trajectories is easy now, given the number crunching power of today’s machines. Companies like Altair, who work in the field of CAE, have gainfully used it to provide software that deals with multi body dynamics.
The objective of kinematics is to develop various means of transforming motion in order to achieve a specific kind needed in applications. For example, let’s assume that an object is to be moved from point A to point B along some path. The first question in solving this problem is usually: is there any mechanism that can be used to perform this function? And the next question: how can such a mechanism be designed?
The objective of dynamics is analysis of the behaviour of a given machine or mechanism when subjected to dynamic forces. In the above example, when the above mechanism is already known, external forces are applied and its motion studied. The determination of forces induced in machine components by the motion is part of this analysis. The role of kinematics is thus to ensure the functionality of the mechanism, while the role of dynamics is to verify the acceptability of induced forces in the mechanism parts.
Multi-body Analysis
We just have taken a very brief overview of Kinematics and Dynamics. Let us now see how they are related to motion analysis of multi-bodies.
The study of multi-body system motion involves both kinematic analysis and dynamic analysis. The kinematic analysis involves the study of the system’s motion without considering the forces that produce this motion. It entails the determination of position, velocity and acceleration of the components that comprise the system. The analysis of the relationship between the motion of the system parts and the forces that causes it is handled by dynamics. It is important to note that the forces include both external applied forces to the multi-body and the internal forces.
Software for Multi-body Analysis
Multi-bodies are complex entities. They are made of several components that can be divided into two major groups – the links (which are nothing but bodies with a convenient geometry), and kinematic joints, which introduce some restrictions on the relative motion of the various bodies of the system. The functionality of a kinematic joint relies upon the relative motion allowed between the connected components, which is not possible without providing certain clearance between the mating parts. This tolerance induces fatigue and vibration in the multi-body, and needs to be considered in motion analysis. Multi-bodies present additional complexities that we will not delve into in this article; suffice it to say that all these complexities make multi-body analysis a difficult task. Before powerful computers were introduced, it was an extremely tedious task to solve the equations involved manually. However, all that has now changed due to the tremendous computing power today’s machines offer. Today, there are highly sophisticated software (like Altair MotionSolve and Altair MotionView) that allows users to quickly build, analyze, and improve mechanical system designs even before physical prototypes are available. And their parametric capabilities facilitate design revision with utmost easy.
Summary
Multi-body analysis is important as many industrial applications depend on accurate analysis of the various forces that act on a system / mechanism, especially systems that involve motion. Sophisticated software available today has helped engineers and designers simulate, analyze and model such complex multi-body environments easily. Thanks to applications like Altair MotionSolve and MotionView, what was once tedious to perform has been simplified and can be solved by anyone without needing any special knowledge of physics or mathematics.