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A 2-D simulation model for lifting activities
Computers ind. Engng Vol. 35, Nos 3-4, pp. 619-622, 1998 © 1998 Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain PIh S0360-8352(98)00173-9 o36o-8352/98 $19.0o + o.oo
Pergamon
A 2-D SIMULATION MODEL FOR LIFTING ACTIVITIES
M.M. Ayoub Department of Industrial Engineering Texas Teeh University Lubbock, TX 79409-3061 USA
ABSTRACT Occupational biomechanics models deal with the evaluation of physical activities such as lifting of loads. This allows the user to determine the stresses imposed on the musculoskeletal system while holding or moving a load. These models are useful tools in estimating these stresses especially those imposed on the lumbar spine, dynamic biomechanical models, as opposed to static models require the displacement-time information to obtain the kinematics needed to estimate the kinetics of the motion. However, the collection of this displacement data is both tedious and can require expensive equipment. Simulation models on the other hand can provide an indirect means of performing the biomechanical analyses without having to collect the displacement-time data. A typical simulation model for 2-D lifting activities will be presented. The basis for this is the hypothesis that the body will perform the activity in such a manner so as to minimize the work done. Using this assumption an objective function was developed subject to a set of constraints. These constraints relate to the human movement, the physical workplace layout, and maintenance of balance. Using this model, it was possible to generate the lifting motion patterns, as well as the kinematics and kinetics of motion. The paper discusses the model development, the model output and the kinematics and kinetics of the simulation of the lifting action. © 1998 Published by Elsevier Science Ltd. All rights reserved. KEYWORDS Simulation, Biomeehanics, Lifting, Optimization, Kinematics, Kinetics INTRODUCTION Manual material handling, particularly lifting, poses a risk to many workers and is considered a major cause of work-related low back pain and impairment. In the interest of reducing work-related injuries by reducing the stresses acting on the human body, ergonomists evaluate these stresses as a task is performed. Biomechanical models are used to quantify the effects of a physical activity on individuals by estimating the forces and moments acting on the musculoskeletal system. Typically the inverse dynamics approach is used to investigate the biomechanical risks associated with a particular lifting task, which requires the collection of displacement-time data as the task is being performed. The data collection process is often costly and difficult to perform since an expensive motion analysis system is required and the data processing itself is tedious and time consuming. Through use of biomechanical simulation, these steps may be greatly reduced and eventually eliminated. A computerized 619
Selected papers from the 22nd ICC&IE Conference
620
dynamic biomechanical simulation model of lifting can be a valuable tool for task analysis and evaluation. Lee (1988), Hsiang (1992), Lin (1995) and Bernard (1995) evaluated several versions of the simulation model based on comparing actual and simulated angular displacement trajectories. METHODS Actual Data Ten subjects, five males and five females, were recruited from the university population to serve as subjects. The mean age of the males was 23 years, with a range of 19 to 27. The maximum acceptable weight limit (MAWL) of each subject was determined in a psychophysical experiment session. The MAWL was used to set standard weights for males and for females to avoid overloading. A twelve task conditions were used. It consisted of two ranges of lift (floor-to-shoulder and floor-to-knuckle), two sizes of box (30.5 cm x 30.5 cm x 30.5 cm and 30.5 cm x 30.5 cm x 45.7 cm in the sagittal plane) and three weights of load (11.5 kg, 16.0 kg and 20.5 kg for males and 4.5 kg, 6.8 kg and 9.1 kg for females). The 36 trials were completely randomized within each subject. Reflective joint center markers were placed on each subject at the following locations: knuckle, wrist, elbow, shoulder, hip, knee and ankle. The subject then lifted the box from the floor and placed it onto a shelf using a freestyle-type lift. A Motion Analysis System recorded each experimental lifting trial at a rate of 100 Hz. Each lift captured by the motion analysis system was tracked and digitized to obtain the x, y coordinates of each reflective marker from which the kinematics and kinetics of the "actual" lifts were estimated using existing 2-D biomechanical models. The Simulation Model The approach proposed by Hsiang (1992) and Lee (1988) in simulating human lifting was modified. In this approach, a basic assumption is used: the human body performs a motion, particularly in high exertion tasks, according to some criterion such as the minimization of total muscular effort. The task under simulation is a symmetrical lift in the sagittal plane. The body is considered as 5 rigid links. The inertial property of each body segment was taken from the literature as compiled in Winter (1990). Using optimization concepts, lifting is assumed to be performed in such a way that it minimizes a non-linear objective function: minimize T 5(
"~, 2
f ~|Mi(t)/ dt i-'oi=l ~, Si(t) )
(1)
where: Si is the moment strength of each joint; Mi is the reactive moment at each joint; and T is the time to perform the lift. The ratio of the joint moment to strength represents the muscular effort exerted at that joint. The ratio is then raised to the second power to increase the penalty for higher deviation of the function from the minimum. The summation of the squared ratio over the 5 joints represents the total muscular effort of the body at one instant during the lift. The time integral of the total muscular effort over the entire period of the lift ensures that the minimization takes into account the complete history of the lift.
621
Selected papers from the 22nd ICC&IE Conference
The model has a non-linear objective function subject to various non-linear constraints. Numerically, constraints serve to reduce the feasible solution space while searching for the optimal answer. The use of a large number of constraints with more complex forms than simple bounds increases the complexity of the optimization problem dramatically. To avoid such problems, a new formulation of the constraints for the lifting optimization model was considered as follows: (1) Joint Mobility constraints Otj,L< Ctj(t) < tXj,U,
j = 1..... 5
0
(2)
where: o~j(t) = included angle of joint j at time t; Ctj,L= minimum included angle of joint j; and otj,o = maximum included angle of joint j. The maximum included angle is the maximum rotational angle in one rotational direction and the minimum included angle the maximum rotational angle in the other direction with a negative sign. Only joint flexion/extension was considered for the planar sagittal lifting motion. (2) Joint moment strength constraints Mj(t) < Sj(t), j = 1..... 5
(3)
where: Sj = the moment strength of joint j, as predicted by Stobbe's equations; and Mj = the magnitude of the moment vector Mj at joint j. The constraints on joint moments describe the strength-limited behavior of human motion. The optimization lifting model is treated at the gross musculoskeletal level. (3) Collision avoidance constraints if {Ybox(t) ~ [y,hdf-( h + 81, Yshelf+ ( h +8)]}
then,
{EXbox(t) +
-~ + 8
- Xshelf < 0
}
(4)
if {Yk,ee(t)~ IYbox(t)" (h + g0, Ybox(t)+ ( h +~)]}
eo,
tx,"
> °t
(5)
where: (x~x(t), Ybox(t))= position of the center of box at time t; (Xk.~(t), Yknee(t))= position of the knee joint at time t; (Xshclr,Yshelf)= position of the edge of shelf; h = height of box in the sagittal plane; 1 = length of box in the sagittal plane; T = total lifting time; 8 = collision tolerance. Equation 4 describes the avoidance of collision between the box and the shelf, while equation 5 describes the collision avoidance between the box and the knee. (4) Postural stability constraint (Xheei + 8) g Xcm g (xtoe + 8)
(6)
where: Xcm horizontal position of the system center of mass; xh~l = horizontal position of the end of foot; xt~ = horizontal position of the tip of foot; 8 = allowance for the thickness due to wearing shoes. The postural stability constraint indicates that the horizontal position of the center of mass of the lifting system, including the person and the box, should not fall outside the foot support area. =
Selected papers from the 22nd ICC&IE Conference
622
RESULTS AND DISCUSSION In order for the simulation to prove useful to ergonomists, it must be shown to accurately predict variables commonly used in ergonomic evaluations. To show that the simulation produced reliable estimates, kinematic and kinetic variables were compared to data obtained from the human subjects in the experiment. Three sets of response variables were analyzed, those related to the goal of the task, the compression force on the spine and the moments at the joints. The response variables related to the goal of the task were the peak vertical velocity of the load (m/s), the peak vertical acceleration of the load (m/s:) and the total distance traveled by the load in moving from the origin to the destination (m). Two compression force variables, the peak static L5/S1 compression force (N) and the peak dynamic L5/S 1 compression force (N), were evaluated. Selected response variables related to the moments at the joints were the objective function value driving the simulation and the peak moment at each of the five body joints. Figure 1 demonstrates that the trajectories predicted by the simulation generally overlap those of the actual lifts; similar overlapping occurred in each response variable. Figure 2 contains a sample scatter plot showing the relationship between the actual and predicted peak compressive force on the low back. REFERENCES Ayoub, M.M. (1993, 1989). Development of a Model to Predict Lifting Motion. NIOSH Grant #R010H2434. Bernard, T.M. (1995). Computerized Dynamic Biomechanical Simulation of Lifting Versus Inverse Dynamics Model: Effects of Task Variables. Ph.D. Dissertation, Dept. of Industrial Engineering, Texas Teeh University, Lubbock, TX. Hsiang, M.S. (1992). Simulation of Manual Material Handling. Ph.D. Dissertation, Dept. of Industrial Engineering, Texas Teeh University, Lubbock, TX. Lee, Y.H.T. (1988). An Optimization Model to Evaluate Methods of Manual Lifting. Ph.D. Dissertation, Dept. of Industrial Engineering, Texas Tech University, Lubbock, TX. Lin, C.J. (1995). A Computerized Dynamic Biomechanical Simulation Model for Sagittal Plane Lifting Activities. Ph.D. Dissertation, Dept. of Industrial Engineering, Texas Tech University, Lubbock, TX. Winter, D.A. (1990). Biomechanics and Motor Control of Human Movement. Second Ed., John Wiley and Sons: New York.
PeakDynamic~preemio~llForce
1
" /
AclualIN} Figurcl. LiftingMotion Pattern
Figure 2. L5/S1 Dynamic Compressional Force Scatter Plot:Predicted versus Actual
Pergamon
A 2-D SIMULATION MODEL FOR LIFTING ACTIVITIES
M.M. Ayoub Department of Industrial Engineering Texas Teeh University Lubbock, TX 79409-3061 USA
ABSTRACT Occupational biomechanics models deal with the evaluation of physical activities such as lifting of loads. This allows the user to determine the stresses imposed on the musculoskeletal system while holding or moving a load. These models are useful tools in estimating these stresses especially those imposed on the lumbar spine, dynamic biomechanical models, as opposed to static models require the displacement-time information to obtain the kinematics needed to estimate the kinetics of the motion. However, the collection of this displacement data is both tedious and can require expensive equipment. Simulation models on the other hand can provide an indirect means of performing the biomechanical analyses without having to collect the displacement-time data. A typical simulation model for 2-D lifting activities will be presented. The basis for this is the hypothesis that the body will perform the activity in such a manner so as to minimize the work done. Using this assumption an objective function was developed subject to a set of constraints. These constraints relate to the human movement, the physical workplace layout, and maintenance of balance. Using this model, it was possible to generate the lifting motion patterns, as well as the kinematics and kinetics of motion. The paper discusses the model development, the model output and the kinematics and kinetics of the simulation of the lifting action. © 1998 Published by Elsevier Science Ltd. All rights reserved. KEYWORDS Simulation, Biomeehanics, Lifting, Optimization, Kinematics, Kinetics INTRODUCTION Manual material handling, particularly lifting, poses a risk to many workers and is considered a major cause of work-related low back pain and impairment. In the interest of reducing work-related injuries by reducing the stresses acting on the human body, ergonomists evaluate these stresses as a task is performed. Biomechanical models are used to quantify the effects of a physical activity on individuals by estimating the forces and moments acting on the musculoskeletal system. Typically the inverse dynamics approach is used to investigate the biomechanical risks associated with a particular lifting task, which requires the collection of displacement-time data as the task is being performed. The data collection process is often costly and difficult to perform since an expensive motion analysis system is required and the data processing itself is tedious and time consuming. Through use of biomechanical simulation, these steps may be greatly reduced and eventually eliminated. A computerized 619
Selected papers from the 22nd ICC&IE Conference
620
dynamic biomechanical simulation model of lifting can be a valuable tool for task analysis and evaluation. Lee (1988), Hsiang (1992), Lin (1995) and Bernard (1995) evaluated several versions of the simulation model based on comparing actual and simulated angular displacement trajectories. METHODS Actual Data Ten subjects, five males and five females, were recruited from the university population to serve as subjects. The mean age of the males was 23 years, with a range of 19 to 27. The maximum acceptable weight limit (MAWL) of each subject was determined in a psychophysical experiment session. The MAWL was used to set standard weights for males and for females to avoid overloading. A twelve task conditions were used. It consisted of two ranges of lift (floor-to-shoulder and floor-to-knuckle), two sizes of box (30.5 cm x 30.5 cm x 30.5 cm and 30.5 cm x 30.5 cm x 45.7 cm in the sagittal plane) and three weights of load (11.5 kg, 16.0 kg and 20.5 kg for males and 4.5 kg, 6.8 kg and 9.1 kg for females). The 36 trials were completely randomized within each subject. Reflective joint center markers were placed on each subject at the following locations: knuckle, wrist, elbow, shoulder, hip, knee and ankle. The subject then lifted the box from the floor and placed it onto a shelf using a freestyle-type lift. A Motion Analysis System recorded each experimental lifting trial at a rate of 100 Hz. Each lift captured by the motion analysis system was tracked and digitized to obtain the x, y coordinates of each reflective marker from which the kinematics and kinetics of the "actual" lifts were estimated using existing 2-D biomechanical models. The Simulation Model The approach proposed by Hsiang (1992) and Lee (1988) in simulating human lifting was modified. In this approach, a basic assumption is used: the human body performs a motion, particularly in high exertion tasks, according to some criterion such as the minimization of total muscular effort. The task under simulation is a symmetrical lift in the sagittal plane. The body is considered as 5 rigid links. The inertial property of each body segment was taken from the literature as compiled in Winter (1990). Using optimization concepts, lifting is assumed to be performed in such a way that it minimizes a non-linear objective function: minimize T 5(
"~, 2
f ~|Mi(t)/ dt i-'oi=l ~, Si(t) )
(1)
where: Si is the moment strength of each joint; Mi is the reactive moment at each joint; and T is the time to perform the lift. The ratio of the joint moment to strength represents the muscular effort exerted at that joint. The ratio is then raised to the second power to increase the penalty for higher deviation of the function from the minimum. The summation of the squared ratio over the 5 joints represents the total muscular effort of the body at one instant during the lift. The time integral of the total muscular effort over the entire period of the lift ensures that the minimization takes into account the complete history of the lift.
621
Selected papers from the 22nd ICC&IE Conference
The model has a non-linear objective function subject to various non-linear constraints. Numerically, constraints serve to reduce the feasible solution space while searching for the optimal answer. The use of a large number of constraints with more complex forms than simple bounds increases the complexity of the optimization problem dramatically. To avoid such problems, a new formulation of the constraints for the lifting optimization model was considered as follows: (1) Joint Mobility constraints Otj,L< Ctj(t) < tXj,U,
j = 1..... 5
0
(2)
where: o~j(t) = included angle of joint j at time t; Ctj,L= minimum included angle of joint j; and otj,o = maximum included angle of joint j. The maximum included angle is the maximum rotational angle in one rotational direction and the minimum included angle the maximum rotational angle in the other direction with a negative sign. Only joint flexion/extension was considered for the planar sagittal lifting motion. (2) Joint moment strength constraints Mj(t) < Sj(t), j = 1..... 5
(3)
where: Sj = the moment strength of joint j, as predicted by Stobbe's equations; and Mj = the magnitude of the moment vector Mj at joint j. The constraints on joint moments describe the strength-limited behavior of human motion. The optimization lifting model is treated at the gross musculoskeletal level. (3) Collision avoidance constraints if {Ybox(t) ~ [y,hdf-( h + 81, Yshelf+ ( h +8)]}
then,
{EXbox(t) +
-~ + 8
- Xshelf < 0
}
(4)
if {Yk,ee(t)~ IYbox(t)" (h + g0, Ybox(t)+ ( h +~)]}
eo,
tx,"
> °t
(5)
where: (x~x(t), Ybox(t))= position of the center of box at time t; (Xk.~(t), Yknee(t))= position of the knee joint at time t; (Xshclr,Yshelf)= position of the edge of shelf; h = height of box in the sagittal plane; 1 = length of box in the sagittal plane; T = total lifting time; 8 = collision tolerance. Equation 4 describes the avoidance of collision between the box and the shelf, while equation 5 describes the collision avoidance between the box and the knee. (4) Postural stability constraint (Xheei + 8) g Xcm g (xtoe + 8)
(6)
where: Xcm horizontal position of the system center of mass; xh~l = horizontal position of the end of foot; xt~ = horizontal position of the tip of foot; 8 = allowance for the thickness due to wearing shoes. The postural stability constraint indicates that the horizontal position of the center of mass of the lifting system, including the person and the box, should not fall outside the foot support area. =
Selected papers from the 22nd ICC&IE Conference
622
RESULTS AND DISCUSSION In order for the simulation to prove useful to ergonomists, it must be shown to accurately predict variables commonly used in ergonomic evaluations. To show that the simulation produced reliable estimates, kinematic and kinetic variables were compared to data obtained from the human subjects in the experiment. Three sets of response variables were analyzed, those related to the goal of the task, the compression force on the spine and the moments at the joints. The response variables related to the goal of the task were the peak vertical velocity of the load (m/s), the peak vertical acceleration of the load (m/s:) and the total distance traveled by the load in moving from the origin to the destination (m). Two compression force variables, the peak static L5/S1 compression force (N) and the peak dynamic L5/S 1 compression force (N), were evaluated. Selected response variables related to the moments at the joints were the objective function value driving the simulation and the peak moment at each of the five body joints. Figure 1 demonstrates that the trajectories predicted by the simulation generally overlap those of the actual lifts; similar overlapping occurred in each response variable. Figure 2 contains a sample scatter plot showing the relationship between the actual and predicted peak compressive force on the low back. REFERENCES Ayoub, M.M. (1993, 1989). Development of a Model to Predict Lifting Motion. NIOSH Grant #R010H2434. Bernard, T.M. (1995). Computerized Dynamic Biomechanical Simulation of Lifting Versus Inverse Dynamics Model: Effects of Task Variables. Ph.D. Dissertation, Dept. of Industrial Engineering, Texas Teeh University, Lubbock, TX. Hsiang, M.S. (1992). Simulation of Manual Material Handling. Ph.D. Dissertation, Dept. of Industrial Engineering, Texas Teeh University, Lubbock, TX. Lee, Y.H.T. (1988). An Optimization Model to Evaluate Methods of Manual Lifting. Ph.D. Dissertation, Dept. of Industrial Engineering, Texas Tech University, Lubbock, TX. Lin, C.J. (1995). A Computerized Dynamic Biomechanical Simulation Model for Sagittal Plane Lifting Activities. Ph.D. Dissertation, Dept. of Industrial Engineering, Texas Tech University, Lubbock, TX. Winter, D.A. (1990). Biomechanics and Motor Control of Human Movement. Second Ed., John Wiley and Sons: New York.
PeakDynamic~preemio~llForce
1
" /
AclualIN} Figurcl. LiftingMotion Pattern
Figure 2. L5/S1 Dynamic Compressional Force Scatter Plot:Predicted versus Actual