Induced Acceleration Analysis of Three-Dimensional Multi-Joint Movements and Its Application to Sports Movements

A knowledge of how muscle forces produce joint rotations is fundamental in all fields of human movement science, including rehabilitation and sports biomechanics. Such knowledge is necessary for improving the diagnosis and treatment of persons with movement disabilities and analyzing the techniques used by high-performance athletes (Zajac and Gordon, 1989). However, it is difficult to intuitively understand how muscle forces produce joint rotations in multi-joint movements because of the complexity of interjoint interactions, especially in three-dimensional (3D) movements. Therefore, although muscle activities, joint torques, and joint rotations themselves have been examined extensively in many sports movements (Barrentine et al., 1998; Elliott et al., 2003; Feltner and Dapena, 1986; Fleisig et al., 1995; Fleisig et al., 1996b; Glousman et al., 1988; Hirashima et al., 2002; Marshall and Elliott, 2000; Matsuo et al., 2001; Nunome et al., 2002; Putnam, 1991; Sakurai et al., 1993; Sakurai and Ohtsuki, 2000; Sprigings et al., 1994), the knowledge about the cause-and-effect relationships between these variables is insufficient. The purpose of this chapter is to provide the framework to properly understand the causeand-effect relationship between joint torques and rotations during sports movements. In fast sports movements such as baseball pitching and soccer kicking, joint rotations occur sequentially from proximal joints to distal joints. This kinematic sequence itself or the underlying kinetic mechanism is often called the “proximal-to-distal sequence,” “kinetic chain,” or “whip-like effect” (Atwater, 1979; Feltner, 1989; Fleisig et al., 1996a; Kibler, 1995; Kindall, 1992; Putnam, 1991). However, the kinetic mechanism has not been properly understood, because previous studies on sports movements have not focused on the fact that a joint rotation is caused by two different mechanisms: instantaneous and cumulative effects. The instantaneous effect is an instantaneous angular acceleration induced by a joint torque at that instant, whereas the cumulative effect is an angular acceleration induced by the entire joint torque and gravity torque history until that instant (Hirashima et al., 2008; Zajac et al., 2002). Because the mechanical causes are clearly different between the two effects in terms of time, clear differentiation is necessary to understand the original cause of each joint rotation and develop effective training programs. In section 2, I will explain the instantaneous effects produced by a joint torque by systematically presenting examples of single-joint movements, multi-joint movements in a two-dimensional (2D) space, and multi-joint movements in a three-dimensional (3D) space. I