# Analytically Derived Three-Dimensional Reach Volumes Based on Multijoint Movements

## Article excerpt

INTRODUCTION

When designing workplaces or control panels, one should place controls within the reach of the operator's arm or foot to ensure ease of reach and to optimize human performance (Chaffin & Andersson, 1991; Das & Behara, 1998; Mital & Karwowski, 1991; Pheasant, 1998). For example, the aviation industry uses anthropometric data for cargo weight minimization and effective utilization of space. The automotive industry requires that anthropometric data of a dynamic or functional type be used to accommodate the driver (Bullock, 1974; Landau, 2000; McFarland, Damon, & Stoudt, 1958; Peacock & Karwowski, 1993).

In designing a workplace, one must cater to a wide range of human body dimensions. Static arm reach measurements, which are taken using conventional and standardized positions, often provide useful information, but only for the tasks that require the human body to be rigid or motionless. Such data cannot be applied to most dynamic situations. For example, how far one can reach depends not only on the length of one's arm but also on shoulder motion, trunk rotation, back bending, and so forth. Thus what is often needed is a set of dynamic measures defining a volume of space that can be attained by a certain population (Li & Xi, 1990).

Approaches to determining reach volume in the past have focused on setting up theoretical foundations and practical methods for body measurements. These issues have been the subject of numerous experimental studies. The range of arm motions has been presented by many authors in various ways, including simple two-dimensional systems (e.g., horizontal reach), two-dimensional systems (e.g., reach in the vertical or horizontal plane), and more complex three-dimensional systems (Bullock, 1974; Das & Behara, 1998; Kennedy, 1964; Li & Xi, 1990; Nowak, 1978; Prokopenko, Frolov, Biryukova, & Roby-Brami, 2001; Woodson, Tillman, & Tillman, 1992).

However, the methods and measuring systems often differ, which makes comparison and application of results difficult. Also, most measurements are confined to Caucasian and Chinese populations. In addition, these findings are mostly limited to arm reach; foot reach typically has not been included. In real-world situations controls are often operated by foot (e.g., in vehicles). Furthermore, previous studies did not consider trunk motion (vertebral motion) when measuring arm reach. Design data that include trunk motion as well as arm and foot reach are therefore needed.

Kee (1993) and Jung, Kee, and Chung (1995) suggested the use of different types of reach volume depending on the joint involved in reach activities. They applied a paradigm of one-degree-of-freedom motion, defined as movement in a single plane. Their results showed statistically acceptable accuracy compared with data obtained from direct body measurements. However, their derived values differed from the real reach volumes because their methods did not account for conditions when several motions occur concurrently at a given joint. Such is the case, for example, with flexion and adduction-abduction, which occur concurrently at the shoulder joint. Therefore, to make the quantification of joint motions more realistic and accurate, a system with eight degrees of freedom for the upper body and six degrees of freedom for the lower body was used in the present study to describe a complex motion that occurs in three different planes.

In order to analytically obtain the three-dimensional (3-D) reach volume of the human body, information about the range of motion (ROM) at specific joints is required as the model input. Joint mobility or flexibility has been studied by many researchers (e.g., Kroemer, Kroemer, & Kroemer-Elbert, 1994; Webb Associates, 1978). Barter, Emmanuel, and Truett (1957) provided representative baseline values for healthy men. …

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