## Biomechanics of Bicep Curls

*April 23, 2011*

*Another dry report compiled for my Ortho class, again may be interesting to some.*

Every day, thousands of American men in gyms across the country perform biceps curls in the mirror. This exercise, commonly referred to as “curls for the girls” is a staple of the modern male resistance training routine. The widespread proliferation of this movement necessitates a deep understanding of the implications on the human body; namely, the forces sustained by the elbow joint and produced by the surrounding muscles in the execution of the movement.

**Analysis**

The body was first simplified into the system shown below.

*Figure 1. System Geometry and Forces [Courtesy S.M.Klisch, Cal Poly, San Luis Obispo]*

This simplification required a few assumptions, most notably that the surrounding bones act as rigid bodies, that the muscles acting around the joint can be expressed as a single linear force, and that the problem can be modeled with the rudimentary geometry presented.

Table 1 offers a quick-reference list of the variable designations.

*Table 1. Variable Designations*

The following values were set as known constants: W=25 N, Forearm weight = 17 N, Forearm lever = 13 cm, and the muscle properties given in Table 2.

*Table 2. Muscle Property Values*

The three basic static equations were constructed from the geometry:

Then the stresses were related to the forces:

Finally, the equations for the parameters to be optimized:

First, equations 1-3 were solved to find each muscle force, and the corresponding joint contact force, when only one muscle is active – for each muscle. Then, all eight equations were expressed in an EES program (code given at bottom). The native EES optimization engine was then used to find the conditions for maximum endurance time (T) and minimum joint contact force (J_{TOTAL}), respectively. The results of all five (3 reduction and 2 optimization) models are given in Table 3.

**Results**

*Table 3. Results*

**Discussion**

The first salient conclusion to be drawn from the results presented in Table 3 is that **it’s critical that this movement is supported with the activation of more than one muscle**, as the stresses any muscle would see if it were acting alone are extremely high (near or well above the 0.45 MPa physiological limit), even with a relatively paltry load.

It is interesting to note that the conditions for maximum endurance and minimum joint force are quite different, **indicating that joint fatigue is not the limiting factor for endurance in this movement**.

On a personal note: *Like other teenage boys, I used to be a big fan of bicep curls. More recently, I’ve gotten all my bicep work in the form of weighted chin-ups, with great results.*

___________________________________

**EES Code**

“Constants”

W_db=25 [N]

r_db=0.3 [m]

W_arm=17 [N]

r_arm=0.13 [m]

r_bic=.043 [m]

r_bra=.032 [m]

r_brr=.027 [m]

A_bic=.00044 [m^2]

A_bra=.00071 [m^2]

A_brr=.00016 [m^2]

theta_bic=78 [deg]

theta_bra=65 [deg]

theta_brr=22 [deg]

“Statics”

SIGMA_M=0

SIGMA_M=W_db*r_db-F_bic*r_bic-F_bra*r_bra-F_brr*r_brr+W_arm*r_arm

SIGMA_F_x=0

SIGMA_F_x=-(F_brr*COS(theta_brr))-(F_bra*COS(theta_bra))-(F_bic*COS(theta_bic))+J_x

SIGMA_F_y=0

SIGMA_F_y=(F_brr*SIN(theta_brr))+(F_bra*SIN(theta_bra))+(F_bic*SIN(theta_bic))-J_y-W_db-W_arm

“Stresses”

sigma_bic=F_bic/A_bic

sigma_bra=F_bra/A_bra

sigma_brr=F_brr/A_brr

{“Endurance Time”

T=((sigma_bic^(3))+(sigma_bra^(3))+(sigma_brr^(3)))^(-1)}

“Minimal Resultant Joint Contact Force”

J_total=SQRT((J_x^2)+(J_y^2))

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