Lecture 20
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Stability and balance refer to an object's ability to resist changes to its equilibrium state and return to its original position if disturbed. Key factors that influence stability include an object's mass/moment of inertia, its base of support, the position of its center of mass relative to the base of support, and surface friction. Static balance requires keeping the center of mass over the base of support, while dynamic balance involves controlling the center of mass during movements to prevent losing equilibrium and falling.
Lecture 20
- 1. Stability and Balance Equilibrium Stability and Balance • an object is at rest and will remain at rest Stability Objectives: • ability to resist a disruption of equilibrium • ability of a body to return to its original state if • Define the concepts of stability and balance disturbed • Define center of mass, center of pressure, base • more stable = able to resist a larger force of support • Understand requirements for static & dynamic Balance balance • the ability to control equilibrium • Understand the 5 factors that influence stability Center of Mass Center of Pressure • Geometric point about which every particle of a • Reaction forces between the body and support body's mass is equally distributed surface are distributed over the entire contact area • The “average” location of the mass of a body • The force can be summed into a single net force acting at a single point: the center of pressure Σ x i mi x head mhead • Center of pressure = point about which the ground x com = Σ mi reaction force is balanced x arm marm x torso Center of • Segment mass x forearm mtorso mforearm xcom Pressure and center of x thigh mthigh mbody mass locations available in x leg mleg anthropometric Fground x foot mfoot tables Fground 1
- 2. Computing Center of Pressure Base of Support • Center of pressure is the point about which the • Base of support: area enclosed by all the points net torque created by the ground reaction forces at which the body contacts a supporting surface is zero • A person can move the center of pressure to any • Example: point within the base of support, but cannot move Center of Pressure it outside the base of support toe F1 = 100 N F2 = 50 N 5 cm 10 cm 15 cm heel ΣT = (0.1 m)(50 N) – (0.05 m)(100 N) = 0 during left during bipedal up on toes feet and hand on foot stance stance of one foot support surface(s) Static Balance Dynamic Balance • To remain in equilibrium, the center of pressure • When center of mass is moving must be directly below the body center of mass forward, must apply posterior- • Thus, to remain in equilibrium, the body center of directed force and torque to arrest mass must be within the boundaries of the base ω anterior motion and rotation before a of support v loss of balance • If moving forward faster Backward Forward → greater decel. impulse needed Balance Balance W → greater displacement during decel. Loss Loss Region W Region → COM must start off more posterior • Greater horizontal distance from a Fgrf boundary of the base of support Line of Gravity → less likely to lose balance in that Base of direction support Fgrf 2
- 3. Factors Increasing Stability Factors Increasing Stability 3. Increased base of support 1. Greater mass and moment of inertia Requires a larger force or torque to accelerate Greater base of → Center of mass can travel support in a farther before crossing the 2. Increased surface friction given direction boundary Friction forces used to prevent or stop horizontal 4. Increased horizontal distance between center motion of mass and base of support boundary Increased friction → Greater ability to resist / stop horizontal motion Center of mass must travel farther before a balance loss; provides more time for deceleration m Fapplied Fapplied - Ffriction dist. for balance loss left ax = m Ffriction ≤ µ N W dist. for balance loss backward dist. for balance loss forward x dist. for balance loss right N=W Factors Increasing Stability Dynamic Stability 5. Lower center of mass height • Many dynamic movements, including walking and running, are unstable Less destabilizing torque produced by a given • Walking and running essentially consist of a angular displacement series of interrupted falls → less opposing torque needed to • Difficult to quantify stability during such tasks restore balance W Path of Center of Pressure T = d⊥ W W d⊥ Path of Center of Mass 3