Biomechanics of Movement | Lecture 6.2: Measuring and Calculating Moments

Understanding Musculoskeletal Geometry and Moments

Defining a Moment

• A moment is a mechanical property defined by the principles of mechanics, specifically concerning the effect of a force about a point (point O).

• The moment M of force F about point O is calculated using the cross product: M = r times F , where r is the vector from point O to any point along the line of action.

Understanding Moment Arms

• A moment arm represents the distance that contributes to mechanical advantage in muscle function. It is defined as:

• Moment arm r = M/|F| cdot z

• This calculation results in a scalar quantity representing how effectively a muscle can generate torque around a joint.

Sources of Musculoskeletal Geometry

• Musculoskeletal geometry can be derived from various methods, including:

• Digitizing anatomical landmarks on skeleton models.

• Utilizing magnetic resonance imaging (MRI).

Static Analysis Example

• In static analysis, we consider forces acting on an arm with weight at its end. For example, balancing a 10 Newton weight requires calculating muscle force based on distances involved.

• The equation for static equilibrium states that the sum of moments equals zero:

• R times F - W times D = 0

Mechanical Advantage Calculations

• Typical ratios show that moment arms are often much smaller than distances to weights; for instance, if distance d = 10cm, and moment arm r = 2cm, then:

• Muscle force required could be significantly higher than the weight being lifted.

• This leads to scenarios where lifting heavier weights results in disproportionately high muscle forces due to low mechanical advantage.

Assumptions in Planar Analysis

• Several assumptions are made during planar analysis:

• The system operates in two dimensions.

• Joints behave like frictionless hinge joints.

• Muscles are modeled as straight lines between attachment points.

Specific Muscle Example: Brachialis

• For muscles like brachialis with specific moment arms (e.g., approximately 2 cm), calculations reveal significant force requirements when lifting weights at greater distances (e.g., d = 25 cm).

Transitioning to Three-Dimensional Analysis

• Moving into three-dimensional analysis involves considering multiple muscles and their contributions through vector equations.

Understanding Muscle Forces and Moment Arms

Overview of Degrees of Freedom in Musculoskeletal Analysis

• The analysis involves three degrees of freedom and three equations, allowing for straightforward estimation of muscle forces through a 3D static analysis.

• While basic scenarios are manageable, complexities arise with multiple muscles, making the problem-solving process more challenging.

Measuring Moment Arms

• Moment arms are defined as the moment divided by the magnitude of muscle force; they can be visualized as the perpendicular distance from the muscle line of action to the joint center.

• An MR image example illustrates how to identify this distance (r), specifically between the ankle joint center and the Achilles tendon.

Techniques for Estimating Moment Arms

• The tendon excursion method is introduced as a technique for estimating moment arms, utilizing principles from virtual work.

• A cadaver limb setup is described where a length transducer measures changes in muscle-tendon length at various joint angles.

Experimental Measurement Process

• In a cadaver model, changes in muscle length during movement can be measured despite lack of active shortening or lengthening due to tissue detachment.

• A mathematical proof assignment will demonstrate that moment arm (r) correlates with changes in muscle-tendon length relative to joint angle variations.

Data Collection and Analysis

• Experimental data collection involves measuring changes in joint angles alongside corresponding changes in muscle-tendon lengths to calculate moment arms.

Muscle Mechanics: Moment Arms and Length Changes

Understanding Moment Arms in Muscles

• A concept test is introduced regarding whether muscles with larger moment arms undergo a greater change in length with joint angle. The answer is confirmed to be true.

• The discussion begins with a simple musculoskeletal system illustration, comparing two muscles: one positioned close to the joint and another further away.

• The muscle closer to the joint has a relatively small moment arm, while the muscle further from the joint possesses a larger moment arm.

• As the configuration changes from extension to flexion, it is noted that the muscle with the smaller moment arm experiences minimal length change compared to the significant length change of the muscle with a larger moment arm.