Degrees of Freedom in Mechanics

Book excerpt: 1: Degrees of freedom (mechanics): This chapter introduces the concept of degrees of freedom, explaining its significance in mechanical systems and how it influences the motion of objects. 2: Machine: Explore the nature of machines, including their structure, function, and the role of degrees of freedom in determining machine behavior and capabilities. 3: Kinematics: Learn the principles of kinematics, focusing on the motion of bodies without considering forces, and its application in robotic systems. 4: Configuration space (physics): Understand the concept of configuration space, where all possible positions and orientations of a system are represented. 5: Rigid body dynamics: Dive into rigid body dynamics, focusing on the motion of solid bodies in a mechanical system and its relevance to robotics. 6: Inverse kinematics: Explore inverse kinematics, a crucial aspect of robotic movement that involves calculating the required joint parameters to reach a target position. 7: Nonholonomic system: Learn about nonholonomic systems, where constraints on movement depend on the velocity, impacting the design of robotic systems. 8: Robot kinematics: This chapter delves into the specific application of kinematics to robots, covering how they achieve movement through joints and links. 9: Linkage (mechanical): Study the mechanical linkages that connect parts of a machine, enabling precise movement and functionality in robotic systems. 10: Overconstrained mechanism: Examine overconstrained mechanisms, which, despite having more constraints than necessary, can still function effectively in some systems. 11: Six degrees of freedom: A focus on the six degrees of freedom crucial to robotic arms and manipulators, enabling full control over movement in threedimensional space. 12: Parallel manipulator: Study the parallel manipulator, a mechanism in which multiple arms work in tandem to control movement with high precision. 13: Multibody system: Understand the dynamics of systems involving multiple interconnected bodies, critical in complex robotic systems. 14: Kinematic pair: Learn about kinematic pairs, which define the relative motion between components in a mechanism and their constraints. 15: Kinematic chain: This chapter discusses kinematic chains, where a series of interconnected links and joints create a system capable of controlled movement. 16: Holonomic constraints: Dive into holonomic constraints, where the restrictions on motion are directly related to the system's coordinates. 17: Chebychev–Grübler–Kutzbach criterion: Explore this criterion for analyzing the degree of freedom in mechanisms and determining the feasibility of mechanical systems. 18: Mechanism (engineering): A deeper look into mechanisms in engineering, focusing on their role in transforming motion within mechanical systems. 19: Kinematics equations: Learn about the mathematical equations that govern the motion of robotic systems, providing solutions to kinematic problems. 20: Freedom and constraint topologies: Study the topological relationships between degrees of freedom and constraints in robotic systems, essential for optimal design. 21: Cartesian parallel manipulators: Explore Cartesian parallel manipulators, which offer high accuracy and speed by using multiple arms arranged in parallel.