E0069 Vehicle Roll Center part 1: Instant Center in Kinematics - EulSeoggy Ko

This is the first video, part 1 in a series of videos explaining the Roll Center. It covers kinematics to help you understand the roll center.
There are three types of mass in a vehicle: sprung mass, unsprung mass, and hybrid mass, which connects the sprung mass and unsprung mass.
There are three types of roll centers that have been used so far. They are kinematic roll center, geometric roll center, and force roll center. Even now, the definition of roll center varies depending on the researchers and writers and there are many cases where it is used incorrectly. When the lateral acceleration is relatively small, these three roll centers coincide with each other.
The roll center definition of SAE International is expressed as 'The roll center is the point in the transverse vertical plane through the wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll.’ What we have to know on SAE Definition are, Roll center is defined using the applied force and the height of the roll center is defined, but there is no mention of its lateral location. The roll center is an important characteristic value that summarizes the important characteristics of the developed suspension. The roll center indicates the location where the lateral force generated from the wheel is transferred to the sprung mass, and therefore it affects the behavior of both the sprung mass and the unsprung mass, so it directly affects cornering.
Roll centers can be found at the front and rear wheels, respectively. First, for the front wheels, it can be found on the cross-section of the vehicle that passes through the centers of the left and right wheels. Similarly, for the rear wheels, it can be found on the cross-section of the vehicle that passes through the centers of the left and right wheels. Therefore, there are two roll centers, one on the front cross-section and one on the rear cross-section. If you connect these two with a straight line, you can get a straight line in the fore-aft direction of the vehicle, and this is called the roll axis.
Let's find out what the roll center means. All recently published vehicle dynamics books commonly point out that the expression roll center is incorrect. When the expression roll center was first used a long time ago, it was borrowed from the expression instant center in kinematics, and it is assumed that the expression roll center was used by removing the instant and replacing it with roll. The reason why this expression is incorrect can be explained as follows. In reality, when a vehicle rolls, it does not rotate around an axis. It also does not rotate around a point. Therefore, if the vehicle is already rolling, it cannot be called a roll center. The roll center is a position defined at a certain moment in the roll motion. Professor Massimo Guiziani uses the expression no roll center instead of roll center in his book Science for Vehicle Dynamics. However, the expression roll center has been used traditionally in the industry and continues to be used without disappearing. Regardless of the appropriateness of the expression, the roll center is an important characteristic that summarizes the developed suspension.
let's look at the types of joints defined in kinematics. Joints are also called pairs. In kinematics, pairs are largely divided into two types: lower pairs and higher pairs. Lower pairs are joints that make surface contact, and higher pairs are joints that make line or point contact. Of course, there are exceptions such as needle bearings, but most can be distinguished by the types of contact. There are six basic joint types in lower pairs. They are revolute, prism, screw, cylinder, sphere, and flat pair. The vehicle's double A arm suspension has eight links and ten joints.
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The mobility of a mechanism is the number of input parameters that must be controlled to bring the device into a particular pose, usually the number of joint variables.
In kitematics, instantaneous centers can be defined in two ways. The first definition uses relative velocities. An instantaneous center is a point in one body about which some other body is rotating either permanently or at the instant. The second definition uses absolute velocity. Instant center is a point common to two bodies having the same linear velocity in both magnitude and direction in each.
There are two types of instant centers. primary instant centers, which can be found visually, and secondary instant centers, which cannot be found visually and require analytical methods to find.
To find secondary instant centers, the Aronhold Kennedy theorem should be used which states that the three instant centers shared by three moving rigid bodies are all on the same straight line whether connected or not. Using Kennedy circles, it is very helpful to determine the number of instant centers and to find the locations of instant centers.