(b)For a man of mass 75.0 kg and height 185 cm calculate the following using standard anthropometric data:
(i)The length of his upper arm.
(ii)The mass of his upper arm.
(iii)The position of the centre of mass of his upper arm relative to the glenohumeral joint.
(iv)The radius of gyration of his upper arm about his glenohumeral joint.
(v)The moment of inertia of his upper arm about his glenohumeral joint.
To answer these questions, we will need to use standard anthropometric data. Anthropometry refers to the measurement of human body dimensions and proportions. It provides data on various body segments, such as the upper arm, which is crucial in biomechanics analysis.
(i) The length of the upper arm:
To calculate the length of the upper arm, we need to know the average proportion of the upper arm length to the total height. According to anthropometric data, the average ratio is approximately 0.245 for adult males. Therefore, we can calculate the length of the upper arm using the following formula:
Length of upper arm = Total height * Upper arm length ratio
Length of upper arm = 185 cm * 0.245
(ii) The mass of the upper arm:
Anthropometric data also provides information on the average percentage of body mass attributed to the upper arm. On average, the upper arm represents about 3.25% of the total body mass. To calculate the mass of the upper arm, we can use the following formula:
Mass of upper arm = Total body mass * Upper arm mass ratio
Mass of upper arm = 75.0 kg * 0.0325
(iii) The position of the center of mass of the upper arm relative to the glenohumeral joint:
Determining the exact position of the center of mass of the upper arm relative to the glenohumeral joint requires more specific data, such as segmental masses distribution. Since anthropometric data often does not provide this level of detail, we will assume that the center of mass of the upper arm is located at the midpoint of the upper arm's length.
(iv) The radius of gyration of the upper arm about the glenohumeral joint:
The radius of gyration refers to the distribution of the mass around an axis. It provides an indication of how the mass is distributed and affects the object's rotational motion. To calculate the radius of gyration, we need to know the moment of inertia and the mass of the upper arm.
(v) The moment of inertia of the upper arm about the glenohumeral joint:
The moment of inertia depends on the mass of the upper arm, its distribution, and its distance from the axis of rotation (glenohumeral joint). Without more detailed anthropometric data, it is challenging to calculate the moment of inertia accurately. It involves complex integrals and mathematical calculations based on the upper arm's shape and mass distribution.
To obtain more precise values for (iii), (iv), and (v), specialized instruments like segmental inertial measurement units or motion capture systems would be required. These tools can accurately measure body segment parameters and provide reliable data for biomechanical analysis.