Experimental BrainResearch
Exp Brain Res (1989) 78:547-556
9 Springer-Verlag1989
A kinematic comparison of single and multijoint pointing movements T.R. Kaminski and A.M. Gentile Department of Movement Science, Box 199, Teachers College, Columbia University, 525 W. 120 St, New York City, NY 10027, USA
Summary. Rapid pointing movements (no accuracy or reaction time requirements) were performed under three conditions which limited motion to the shoulder, elbow or a combination of these two joints. Velocity profiles of the hand's trajectory differed during single and multijoint movements. For the same magnitude of displacement, the hand always had a higher peak velocity, shorter rise time (time to peak velocity) and shorter movement time during single joint movements. However, when the profiles were normalized with respect to amplitude and movement time, no significant differences were observed between these three movement conditions. The velocity profiles of the elbow and/or shoulder were also compared under single and multijoint movement conditions. Analysis of these profiles revealed that the relationships between peak velocity and displacement and between movement time and displacement remained the same at the shoulder joint during single and multijoint movements. In contrast, the elbow joint velocity profiles were significantly affected by movement conditions. These relationships (peak velocity/ displacement and movement time/displacement) changed during multijoint movements and became the same as those observed at the shoulder joint. The shape of the hand velocity profile and its invariance across movement conditions can best be explained by dynamic optimization theory and supports the notion that movement of the hand is of primary importance during rapid pointing. However, the consistency of the shoulder velocity profile and the highly significant relationships between the movement of the elbow and shoulder joints indicates that a subordinate joint planning strategy is also used. The purpose of this strategy is to functionally decrease the available degrees of freedom Offprint requests to." T.R. Kaminski (address see above)
and to simplify coordination between the moving joints. Thus, the organization of arm movements is hierarchically structured with important, but different contributions being made on both the hand planning and joint planning levels. Key words: Human arm movement - Velocity profile
Introduction
Multijoint arm movements "have been analyzed from two perspectives: movement of the hand and motion of the individual joints. Assessment of the hand's trajectory has demonstrated that the hand takes a relatively straight path to a target and its velocity profile is smooth and bell-shaped (Morasso 1981; Soechting and Lacquaniti 1981; Abend et al. 1982; Kaminski and Gentile 1986). Analysis of joint motion (shoulder and elbow) has focused primarily on the relationships between the individual joints. Such studies have demonstrated that the relationship between peak velocity and displacement is linear and the same for both joints (Kaminski and Gentile 1986) and that the elbow and shoulder velocities are related to each other as the final position is approached (Soechting and Lacquaniti 1981; Lacquaniti and Soechting 1982). The primary purpose of this study was to determine whether the velocity profiles observed during a multijoint movement are altered when the movement is decomposed into its component parts. More specifically, multijoint movements involving the shoulder and elbow joints were compared with movements produced by elbow or shoulder motion in isolation (single-joint elbow or single-joint shoulder movement). Velocity profiles of the hand's trajectory as well as those of the elbow and
548
shoulder joints were analyzed during single and multijoint movement conditions. We sought to identify the kinematic invariances that persisted during both types of movement as they may be the prime elements from which arm movements are composed. There is little information available concerning the similarities of the hand's trajectory during single and multijoint movement. Obviously, hand path will differ during both types of movement; during single-joint movements hand paths must be curved, while during multijoint movements the hand can traverse innumerable paths. However, the velocity profiles are free to vary under both conditions. Consequently, when assessing how the movement conditions affected the trajectory of the hand, emphasis was placed on comparison of velocity profiles. The velocity profiles of the shoulder and elbow joints were expected to differ when comparing angular motion of these joints under single and multijoint conditions. It has been established that the elbow and shoulder joints are coupled both kinematically (Kaminski and Gentile, 1986) and inertially (Lacquaniti and Soechting, 1982) during multijoint movements. The kinematic coupling may be merely coincidental as the movement characteristics observed at the shoulder and elbow joints during multijoint movement may be the same as those observed during single-joint movement. Movement of the two joints may simply be summated to produce a multijoint movement. Alternatively, the coupling may be a product that is unique to the interaction between the shoulder and elbow joints when motion is occurring at both joints simultaneously. The latter possibility is supported by the fact that interactional forces are present only during multijoint movements and results in an inertial coupling between the elbow and shoulder joints. Consequently, interactional forces partially determine the motion of both of these joints during multijoint movements, but have no effect during single-joint movements. The results of the present study indicated that the movement conditions altered hand velocity when arm movements are performed as fast as possible: the hand moved fastest during singlejoint elbow movements and slowest during multijoint movements. However, the shape of the hand velocity profiles was the same across movement conditions. Analysis of the joint kinematics showed that velocity at the elbow decreased during multijoint movements. Furthermore, motion at the elbow joint appeared to be constrained by motion at the shoulder joint: angular velocity at the shoulder
joint remained the same during single and multijoint movements while angular velocity at the elbow joint decreased during multij oint movements so that the relationship between peak velocity and displacement was the same at both joints. Methods Subjects A total of eight right-handed male and female volunteers between the ages of 20 and 45 with no known history of neuromuscular impairments of the upper extremities served as subjects.
Apparatus The subjects were seated in a cushioned, straight-back chair. The right arm was strapped to a two-degrees-of-freedom manipulandum which permitted shoulder abduction/adduction and elbow flexion/extension in the horizontal plane (see Fig. 1). The upper arm was supported by a molded plastic cuff that was bolted to the manipulandum and prevented arm motion other than through the axis of rotation. The forearm was supported by a Velcro strap attached to the manipulandum and the hand rested on an adjustable hand grip positioned across the heads of the first metacarpal joints. The index finger was strapped to an extension of the hand grip that maintained the finger in full extension and prevented abduction/adduction. The apparatus was composed of an aluminium alloy frame with two stainless steel ballbearing joints and could be adjusted for variations in subject height and arm length. Elbow motion was unrestricted throughout its range of motion while the shoulder joint permitted a 90 deg range of motion in horizontal adduction. The apparatus could be locked to maintain the shoulder joint in positions of 40, 55 and 70 deg horizontal adduction (0 deg horizontal adduction is the position in which a straight line is formed by the intersection of the two shoulder joints and the elbow) and the elbow joint in positions of 50, 65 and 80 deg flexion (0 deg flexion is the position in which forearm forms a straight line with the upper arm). When correctly adjusted, one ballbearing joint was positioned over the axis of rotation of the shoulder joint, and the other over the axis of the elbow joint. A goniometer was attached above and aligned with the axis of each of the two ball bearing joints to permit accurate visual reading of joint angle. Voltage comparator circuits detected when the shoulder and elbow joints were in the correct starting position which was indicated by the activation of an electric buzzer. The target was displayed as a 2 cm diameter hole in the center of a 4 cm square piece of cardboard.
Procedures Each subject was tested under experimental conditions involving all combinations of the three variables: movement condition (single and multijoint), joint (shoulder and elbow), and displacement (30, 45 and 60 deg). Nine target locations (illustrated in Fig. 1) reflected all combinations of the three amplitudes of shoulder displacement with the three amplitudes of elbow displacement. All multijoint movements were initiated from the same position: 10 deg shoulder horizontal adduction, 110 deg elbow flexion (this position is illustrated in Fig. 1). For single joint movements, one of the joints was locked in each of three positions (40, 55 or 70 deg horizontal adduction for the shoulder and 80, 65 or 50 deg flexion for the elbow) while the free joint moved through randomized displacements of 30, 45 and 60 deg.
549
m
9
B
ted to maintain the arm in that position (approximately 2 s) until told to return to the starting position.
Data collection and reduction L
,
J
Fig. 1. Top view of two degrees-of-freedom pointing manipulandum. Goniometers (G) and potentiometers (P) were positioned above friction-free ball-bearing joints. Arm is in the starting position used for all trials (10 deg shoulder horizontal adduction, 110 deg elbow flexion). The solid squares in front of the subject represent the nine target locations to which the subject had to move the index finger
The positions of the locked joint corresponded to the three final positions that would have been attained at the completion of a multijoint movement. The moving joint under single joint movement conditions always initiated movement from the same position: 10 deg horizontal adduction for shoulder movement and 110 deg flexion for elbow joint movement. To minimize carryover effects, the experiment was conducted in three separate sessions. Multijoint movements were performed on one day, single-joint elbow movements on a second day, and single-joint shoulder movements on a third day (the order of single-joint/multijointand of shoulder/elbow was counterbalanced across subjects). On each day, data were collected on five trials for each of the nine target locations. During the initial part of each session, the apparatus was adjusted to the subject's height and arm length. Although the nine target locations varied depending on the subject's arm length, the locations were the same for each subject on each day of testing. During all trials, both feet were flat on the floor and the left hand rested on the left knee. The subject was instructed to point as fast as possible without making movement corrections (no accuracy requirements). The sound of a buzzer indicated to the subject and the experimenter that the correct initial position had been achieved and the trial could begin. The subject made twenty practice movements to one of the nine target locations before data from five test trials were recorded. This sequence of twenty practice trials followed by five test trials was repeated for all nine target locations. Following a variable foreperiod (one to three seconds), the experimenter depressed a microswitch which initiated data collection. The audible click produced by microswitch closure also served as the "go" signal for the subject. No reaction time requirements were imposed. Microswitch closure also initiated data collection by the computer during the test trials. After completing the movement, the subject was instruc-
Voltage changes from calibrated precision potentiometers mounted above the two ball bearing joints were converted to digital form by an A/D converter, then sampled by a microprocessor and stored on disks at a rate of 200 samples/s for data reduction and analysis. Displacement data were computed then mathematically smoothed using a least squares, third order polynomial technique (microcomputer data smoother program by Dynacomp, P.O. Box 162, Webster, New York) and differentiated to obtain velocity and acceleration characteristics of the movement. Torque data were obtained using inverse dynamic formulations (Hollerbach and Flash 1982). The moment of inertia of the apparatus was determined using the compound pendulum method and found to range from 0.029 to 0.06 kg- m 2 for the proximal segment and 0.0025 to 0.0037 kg - m 2 for the distal segment, depending on the adjustments made for each subject's arm length. The moment of inertia of each subject's upper and lower arm segments were derived from Dempster's (1955) estimates. Analysis Correlation and regression analyses were the primary means of data analysis. Six dependent variables were used in the regression analyses: 1) peak velocity, 2) velocity rise time (time from movement onset to peak velocity), 3) movement time, 4) the time difference between shoulder and elbow movement onset, 5) peak shoulder joint torque and 6) elbow joint torque at the time of peak shoulder torque. Onset time of joint movement was defined as the time when joint angular velocity exceeded 2 deg/s. Similarly, movement time was defined as the first time that angular velocity fell at both joints below two deg/s. Thus, any oscillation of the arm near the completion of the movement was eliminated from the analyses. Difference in onset time was defined as time of movement onset at the elbow minus time of movement onset at the shoulder. Because elbow joint torque was extremely variable, frequently did not reach a positive value and could have multiple peaks, peak elbow torque was not considered an appropriate indicator of forces acting across the elbow joint. Hence elbow joint torque at the time of peak shoulder joint torque was used instead. Variables used in the regression analyses depended on the type and function of analysis performed. When examining joint kinematics, peak angular velocity, velocity rise time and movement time of the individualjoints were assessed. When considering hand kinematics, linear peak velocity, rise time and movement time of the hand were used in the analyses. To eliminate the effect of between subject differences, each subject's scores were standardized by converting to z scores. This conversion permitted scores across subjects to be grouped together without inflating standard deviations. Thus, sample size was the total number of usable trials summed across subjects. Each of the dependent variables was regressed on the independent variables of displacement, movement condition (single or multijoint),joint (shoulder or elbow) and their interaction: displacement X movement condition or displacement X joint. Because the relationship between displacement and each of the dependent variables was the primary focus of attention, displacement was forced to enter the stepwise analysis first. Whether movement condition or the interaction variable entered the analysis next was determined by which one accounted for the greater amount of the remaining unexplained variance.
550 Table 1. Summary of three stepwise regression analyses of hand kinematics during shoulder only and multijoint movements Dependent variable
Peak velocity Rise time Movement time
Explained variance
Total
Linear displacement
Movement condition (shoulder/multi)
Interaction (D X MC)
%*
F
%
F
%
F
92.5 40.3 51.0
1827.04 50.53 265.00
4.3 33.7 20.6
193.28 95.47 38.55
NS NS 2.8
16,26
(%)
96.8 86.0 74.4
* Percent of explained variance Sample size = 700 trials All reported F values have p < 0.01 NS: not significant
Results
The results of the experiment are reported in four sections. First, a determination was made as to whether movement conditions (single or multij oint) affected the velocity profile of the hand's trajectory. Second, the effect of movement conditions on the velocity profiles of the shoulder and elbow joints was analyzed. In the third section, relationships between the kinematic variables of the elbow and shoulder joints were assessed. As velocity rise time was found to have high variability under multijoint movement conditions, a more complete analysis of this variable is presented in the last section.
Hand kinematics during single and multijoint movements Under all movement conditions, a strong linear relationship was observed between linear displacement of the hand and the numerical descriptors of the velocity profiles (peak linear velocity, velocity rise time and movement time). The correlation between displacement and each of the descriptors was always greater than 0.85. However, movement conditions had a marked effect on the kinematics. Given the same magnitude of displacement, peak velocity of the hand was greatest during single-joint elbow movements and was least during multijoint movements. In accord with this observation, rise time (i.e. time to peak velocity) and movement time were longest during multijoint movements. These differences are illustrated in Fig. 2A where the linear displacements of the hand were similar for each of the three velocity profiles shown (singlejoint elbow, single-joint shoulder and multijoint). It is obvious from Fig. 2 that the hand velocity profiles generated during single-joint elbow movements differ from those in the other two movement
conditions. The difference between the velocity profiles generated during single-joint shoulder motion and multijoint motion is smaller. To determine whether an actual difference did exist between these profiles, three regression analyses were performed. Table 1 summarizes the results of these regression analyses in which the effect of movement condition (single-joint shoulder or multijoint movement) was determined for three dependent variables (peak velocity, rise time and movement time). As can be seen in the table, movement condition had a statistically significant effect on all three velocity profile descriptors. Peak velocity was significantly higher, and both rise and movement times were briefer during single-joint shoulder movements. (Although most of the variance in peak velocity was accounted for by displacement, the probability of movement condition affecting peak velocity was greater than 0.99. Thus indicating the importance of movement condition on peak velocity.) Although there are significant quantitative differences in the velocity profiles illustrated in Fig. 2, the shape of the profiles are similar. In order to compare the shapes of the velocity profiles, normalization procedures were performed to remove the effects of maximal speed and time. Normalization was accomplished by converting actual time values to per cent of movement time completed and actual velocity values to per cent of peak velocity. The profiles illustrated in Fig. 2B are the normalized version of those shown in Fig. 2A. Note the substantial overlap. To determine whether the normalized profiles were significantly different from each other, per cent of peak velocity was obtained at 25, 50 and 75 per cent of movement time. Regression analysis was then performed to determine whether movement conditions affected the per cent of peak velocity at each of these movement times. No statistically significant differences
551 HAND VELOCITY PROFILES
A
SHOULDER JOINT VELOCITY PROFILES
o. tv~
SINGLE JOINT MULTIJOINT . . . . .: /
"
SINGLE JOINT NIJLTIJOINT
/),,,
i . 100
TIMEIN MS
kN%-.~
100
v
,
200
TIME IN MS
Fig. 4. Velocity profiles in which the elbow joint had an angular displacement of 44 (top) or 58 (bottom) deg. Each of the profiles represents an ensemble average of elbow movement for one subject under a single or multijoint movement condition. Note that the profiles were different under single and multijoint conditions. Although most elbow profiles were smooth and bellshaped (top), movement under some multijoint conditions resulted in alterations of the characteristic shape (bottom)
under a multijoint condition. For all subjects, the elbow had much higher peak velocities and briefer movement times during single-joint movements than during multijoint movements. In addition, movement conditions affected the form of the velocity profiles. Although the profiles appeared smooth and bell-shaped during all single-joint elbow movements, the acceleration phase (motion before peak velocity) was altered during multijoint movements in that the rate of rise was prolonged and variable and there were additional points of inflection in the velocity profile (see Fig. 4, bottom). Regression analysis comfirmed the observation that movement condition affected the elbow joint kinematics. Peak velocity decreased and movement time increased during multijoint movements. These aspects of the velocity profile were also found to be linearly related to displacement under both single and multijoint movement conditions. In contrast, rise time was linearly related to displacement only
under single-joint conditions. The correlation between displacement and rise time for the singlejoint movement conditions was 0.82 and decreased to 0.02 for the multijoint conditions. Thus, other factors besides displacement must account for the variability in rise time at the elbow joint under multijoint movement conditions. Comparison of elbow and shoulder kinematics. The velocity profiles of the shoulder were similar under single and multijoint movement conditions, whereas those of the elbow joint were not. The total amount of explained variance in peak velocity was the same for both the elbow and shoulder joints. However, the way the variance was partitioned was quite different. For shoulder joint movement, displacement accounted for all of the explained variance, regardless of the type of movement. In contrast, only part of the variance in elbow peak velocity could be explained by displacement while the remainder was explained by movement condition. Similar findings were observed for movement time. Whereas shoulder movement time was not affected by movement condition, the elbow was significantly affected. Thus, movement conditions (single or multijoint) had only minor effects on the velocity profiles at the shoulder joint, but had major effects at the elbow joint.
Relationships between elbow and shoulder joint kinematics across movement conditions
Kaminski and Gentile (1986) previously reported that the relationship between peak velocity and displacement was the same for the elbow and shoulder joints during multijoint movements. To determine whether this similarity was merely coincidental, regression analysis was used to compare the kinematics under single and multijoint movement conditions. Significant F values for the independent variable, joint (the joint at which movement occurred), were observed and indicated that the kinematics of the elbow and shoulder were quite different. Comparison of the Y-intercepts of the shoulder and elbow regression lines under the single joint movement condition indicated that peak velocity was higher and movement time and rise time were briefer for the elbow joint, given the same magnitude of joint displacement. During multijoint movements, the kinematics changed dramatically. The relationship between peak velocity and displacement as well as movement time and displacement was the same for both joints. Although elbow rise time was not related to magnitude of
553 SINGLE JOINT MOVEMENT
Table 2. Summary of two stepwise multiple regression analyses using shoulder and elbow rise times as the dependent variables Step
ooo
Independent variable
Shoulder rise time
no.
SHOULDER ELBOW
. . . .
e~
/./
i \v
1oo
R
Rz
F
0.603 0.766 0.807 0.819
I 15.47 51.85 15.73 5.07
1 2 3 4
Elbow rise time Difference in onset time Elbow peak velocity Elbow displacement
0.777 0.875 0.898 0.905
Step
Independent variable
Shoulder rise time
~"
200
TIME IN M S
no.
M U L T I J O I N T MOVEMENT
1 2 3 4
Shoulder rise time Difference in onset time Shoulder torque Elbow displacement
R
R2
F
0.777 0.810 0.840 0.862
0.603 0.655 0.705 0.716
115.47 I 1.38 12.48 7.18
Sample size = 349 trials All reported F values have p
