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Dynamics Review
Published in Donald E. Carlucci, Sidney S. Jacobson, Ballistics, 2018
Donald E. Carlucci, Sidney S. Jacobson
We will now examine the kinematics of a particle. Kinematics is the study of the motion of particles and rigid bodies without regard to the forces which generate the motion. Particle kinematics assumes that a point can represent the body. The rotations of the particle itself are neglected making this a three-degree-of-freedom model. If we have the inertial reference frames x, y, and z, the position of a particle P is defined by a position vector r drawn from the origin to the particle as shown in Figure 8.5.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
Kinematics is the study of the geometry of rigid body motion without reference to what causes the motion. Kinematic analyses are conducted to establish relationships between the position, velocity, and acceleration of rigid bodies or points on a rigid body.
Mathematical Models of Robot Motion
Published in Jitendra R. Raol, Ajith K. Gopal, Mobile Intelligent Autonomous Systems, 2016
To evaluate any design of a robot by simulation, the kinematic and dynamic mathematical models of the robot including its physical characteristics are required. Several related mathematical tools and algorithms are also required for: (i) spatial localization, (ii) rotation matrix, (iii) homogeneous transformation matrix and its composition, (iv) robot dynamics algorithms, (v) robot system identification, (vi) robot simulation, (vii) optimization algorithms and (viii) robot/arms/links control algorithms [1–16]. In this chapter, basic kinematics and dynamic models for robot/rigid body are studied. In general, the mathematical kinematic model is obtained to implement the simulation of, say biped’s, robot kinematic, and the kinematics model is obtained by homogeneous transformation matrix applying the Denavit Hartenverg (DH) method [1]. Forward and inverse kinematic transformations also play an important role in robot kinematics. Next, we discuss terms that are used frequently in the literature on robot modelling. The kinematics is the study of motion of an object without considering the effect of forces acting on it. The term degrees of freedom (DoF) implies the number of independent position variables needed in order to completely specify motions of a robot. Robot can have an extended DoF because of the extra robot arms, as extensions. A robotic manipulator is a collection of links that are interconnected by flexible joints. At the end of the robot there is a tool or end effector. The robot workspace is defined as the volume of space which can be easily reached by the end effector. The dexterous workspace is defined as the volume of the space where the end effector can be arbitrarily oriented and/or positioned. The reachable workspace is a volume of space which the robot can reach in at least one orientation. The kinematic problem is a mathematical description of the position and orientation of the links of robot, including its legs and arms with respect to time. The position and orientation of an end effector with respect to a reference coordinate system can be computed for given joint angle and link parameters. This is referred to as forward or direct kinematic problem. The computation of the link joint angles for a given position and orientation of the end effector and link parameters is referred to as an inverse kinematic problem.
An Empirical Comparison between the Effects of Normal and Low Vision on Kinematics of a Mouse-Mediated Pointing Movement
Published in International Journal of Human–Computer Interaction, 2022
Yuenkeen Cheong, Chen Ling, Randa Shehab
One way to characterize the process of a pointing movement is through its kinematics. Kinematics is the study of motions without considering the forces that cause the motion. The kinematic approach has been reported in several studies involving computer input devices (Phillips et al., 2005; Slocum, Chapparo et al., 2005; Slocum, Thompson et al., 2005) The literature reports a number of different kinematic measures, which generally fall into two classes: structural and temporal. Structural kinematics measures are usually expressed in spatial units such as distance and amplitude (see Table 1). Common structural kinematics measures are peak velocity (PV), peak acceleration (PA), and proportion of distance traveled at peak velocity (PropDPV). Temporal measures, as shown in Table 2, are time-based, namely: time to peak velocity (TPV), time from peak velocity until the end of movement (TPVEnd), proportion of time to peak velocity (PropTPV), time until peak acceleration (TPA), and proportion of time to peak acceleration (PropTPA). Typical kinematic profiles of a mouse-mediated pointing movement, as well as annotation of common kinematic landmarks, are shown in Figure 1. When divided into primary/secondary submovement based on the SOS paradigm, kinematic measures related to the primary submovement include PV, PropDPV,TPV, and PropTPV. And the kinematic measure that describes the secondary submovement includes time from TPVEnd.
Concussion biomechanics, head acceleration exposure and brain injury criteria in sport: a review
Published in Sports Biomechanics, 2022
Kinematics is the area of mechanics concerned with the motion of an object without reference to the forces that cause the motion (Schmitt et al., 2004). For many years, biomechanical research has focused on understanding the response of the brain to head kinematics and how this relates to brain injury (Zhan et al., 2021). Although the direct relationship to injury is still debated (Meaney et al., 2014; Rowson et al., 2018; Zhan et al., 2021), many brain injury criteria have been developed (Table 1). Although it is not the intention of the author to discuss each brain injury criteria in detail (instead, see Zhan et al. (2021)), it is clear that as research has progressed, brain injury criteria have moved away from focusing specifically on linear acceleration, and instead moved towards angular kinematics. Additionally, more recent metrics tend to utilise various finite element (FE) brain models and take into consideration the components of the resultant vector (i.e., directionality), frequency content and time-pulse (through the use of lumped-parameter models) rather than just peak values of the kinematic measure (Zhan et al., 2021). The vast array of brain injury criteria seen in Table 1 illustrates the complexity of assessing brain injury from head kinematics. Many brain injury criteria may be limited by the relatively poor validity of biomechanical approaches undertaken to develop them. Further limitations include low concussion/brain injury sample sizes, oversampling of non-independent, non-injurious impacts as well as issues such as injury underreporting, diagnostic accuracy and the accumulative effect of preceding HAE (G. Siegmund et al., 2021). These limitations pose the question as to whether these brain injury criteria are valid or clinically relevant. These limitations may be the reason why the majority of studies report only peak resultant kinematic magnitudes (e.g., linear acceleration, angular acceleration and angular velocity) of concussive impacts and HAE in sport, on the basis that higher magnitude events are more severe even though peak resultant magnitudes do not account for important head kinematic signal characteristics such as directionality, frequency content and pulse duration that likely influence brain injury risk. The biomechanical approaches utilised to develop brain injury criteria in a sporting context will be reviewed later in this article .