constraints in the case of rigid body is known as
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Explanation:
Rigid body dynamics are traditionally formulated by Lagrangian or Newton-Euler methods. A particular state space form using Euler angles and angular velocities expressed in the body coordinate system is employed here to address constrained rigid body dynamics. We study gliding and rolling, and we develop inverse systems for estimation of internal and contact forces of constraint. A primitive approximation of biped locomotion serves as a motivation for this work. A class of constraints is formulated in this state space. Rolling and gliding are common in contact sports, in interaction of humans and robots with their environment where one surface makes contact with another surface, and at skeletal joints in living systems. This formulation of constraints is important for control purposes. The estimation of applied and constraint forces and torques at the joints of natural and robotic systems is a challenge. Direct and indirect measurement methods involving a combination of kinematic data and computation are discussed. The basic methodology is developed for one single rigid body for simplicity, brevity, and precision. Computer simulations are presented to demonstrate the feasibility and effectiveness of the approaches presented. The methodology can be applied to a multilink model of bipedal systems where natural and/or artificial connectors and actuators are modeled. Estimation of the forces is accomplished by the inverse of the nonlinear plant designed by using a robust high gain feedback system. The inverse is shown to be stable, and bounds on the tracking error are developed. Lyapunov stability methods are used to establish global stability of the inverse system.
Answer: Two or more rigid bodies in space are collectively called a rigid body system. We can hinder the motion of these independent rigid bodies with kinematic constraints. Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid body system.
Explanation: Step :1 A body that does not deform or alter shape is idealised as a hard body. Formally, it is described as a group of particles with the feature that their distance from one another does not change as the body moves. A rigid body system is a collection of two or more rigid bodies in space. Kinematic constraints allow us to restrict the motion of these independent rigid bodies. The degrees of freedom in a rigid body system are reduced by kinematic constraints, which are restrictions between rigid bodies.
Step :2 It is obvious that rigid body motion is holonomic and scleronomic from the formula for it given above. so A stiff body experiences both holonomic and scleronomic constraint. A mechanical system is scleronomous if the equations of constraints can be expressed in terms of generalised coordinates and the equations of constraints do not explicitly include time. Scleronomic constraints are the name given to such restrictions. Rheonomous is the polar opposite of scleronomous.
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