Abstract: A system that measures a swing of a bat with one or more sensors and analyzes sensor data to create swing quality metrics. Metrics may include for example rotational acceleration, on-plane efficiency, and body-bat connection. Rotational acceleration measures the centripetal acceleration of the bat along the bat's longitudinal axis at a point early in the rotational part of the swing; it is an indicator of the swing's power. On-plane efficiency measures how much of the bat's angular velocity occurs around the swing plane, the plane spanned by the bat and the bat's sweet spot velocity at impact. Body-bat connection measures the angle between the bat and the body tilt axis, which is estimated from the trajectory of the hand position on the bat through the swing; an ideal bat-body connection is near 90 degrees. These three swing quality metrics provide a simple and useful characterization of the swing mechanics.

Abstract: A system that measures a swing of a bat with one or more sensors and analyzes sensor data to create swing quality metrics. Metrics may include for example rotational acceleration, on-plane efficiency, and body-bat connection. Rotational acceleration measures the centripetal acceleration of the bat along the bat's longitudinal axis at a point early in the rotational part of the swing; it is an indicator of the swing's power. On-plane efficiency measures how much of the bat's angular velocity occurs around the swing plane, the plane spanned by the bat and the bat's sweet spot velocity at impact. Body-bat connection measures the angle between the bat and the body tilt axis, which is estimated from the trajectory of the hand position on the bat through the swing; an ideal bat-body connection is near 90 degrees. These three swing quality metrics provide a simple and useful characterization of the swing mechanics.

Abstract: A system that measures a swing of a bat with one or more sensors and analyzes sensor data to create swing quality metrics. Metrics may include for example rotational acceleration, on-plane efficiency, and body-bat connection. Rotational acceleration measures the centripetal acceleration of the bat along the bat's longitudinal axis at a point early in the rotational part of the swing; it is an indicator of the swing's power. On-plane efficiency measures how much of the bat's angular velocity occurs around the swing plane, the plane spanned by the bat and the bat's sweet spot velocity at impact. Body-bat connection measures the angle between the bat and the body tilt axis, which is estimated from the trajectory of the hand position on the bat through the swing; an ideal bat-body connection is near 90 degrees. These three swing quality metrics provide a simple and useful characterization of the swing mechanics.

Abstract: A system that measures a swing of a bat with one or more sensors and analyzes sensor data to create swing quality metrics. Metrics may include for example rotational acceleration, on-plane efficiency, and body-bat connection. Rotational acceleration measures the centripetal acceleration of the bat along the bat's longitudinal axis at a point early in the rotational part of the swing; it is an indicator of the swing's power. On-plane efficiency measures how much of the bat's angular velocity occurs around the swing plane, the plane spanned by the bat and the bat's sweet spot velocity at impact. Body-bat connection measures the angle between the bat and the body tilt axis, which is estimated from the trajectory of the hand position on the bat through the swing; an ideal bat-body connection is near 90 degrees. These three swing quality metrics provide a simple and useful characterization of the swing mechanics.

Abstract: A method for analyzing sensor data from baseball swings (or swings in similar sports) that transforms data into a reference frame defined by the bat orientation and velocity at impact. The trajectory of the sweet spot of the bat is tracked through the swing, and is analyzed to generate metrics describing the swing. A two-lever model of the swing may be used to model the effects of body rotation and wrist rotation. Data may be analyzed to identify relevant events during the swing such as start of downswing, commit (wrist release), on-plane, peak bat speed, and impact. Illustrative swing metrics derived from the sweet spot trajectory, the swing plane reference frame, and the two-lever model include: forward bat speed, on-plane rotation, hinge angle at commit, hinge angle at impact, body rotation ratio, body tilt angle, and swing plane tilt angle.

Abstract: A method for analyzing sensor data from baseball swings (or swings in similar sports) that transforms data into a reference frame defined by the bat orientation and velocity at impact. The swing plane defined by these two axes provides a natural and robust reference frame for physically relevant measurements of swing characteristics. Illustrative swing metrics derived from swing plane reference frame data include: swing speed, defined as a rotational rate within the swing plane; total swing angle, defined as the angular change within the swing plane; and swing tempo, defined as the percentage of peak swing speed achieved halfway through the swing. Analyzing these metrics from multiple swings across multiple users identifies factors that contribute to peak performance. Metrics may be combined into multidimensional feature vectors that characterize a swing; these feature vectors may be used to group swings into swing styles or to match swings against similar players.

Abstract: A system that measures a swing of a bat with one or more sensors and analyzes sensor data to create swing quality metrics. Metrics may include for example rotational acceleration, on-plane efficiency, and body-bat connection. Rotational acceleration measures the centripetal acceleration of the bat along the bat's longitudinal axis at a point early in the rotational part of the swing; it is an indicator of the swing's power. On-plane efficiency measures how much of the bat's angular velocity occurs around the swing plane, the plane spanned by the bat and the bat's sweet spot velocity at impact. Body-bat connection measures the angle between the bat and the body tilt axis, which is estimated from the trajectory of the hand position on the bat through the swing; an ideal bat-body connection is near 90 degrees. These three swing quality metrics provide a simple and useful characterization of the swing mechanics.

Abstract: A method that estimates the 3D trajectory of a projectile, such as a golf ball or baseball, by analyzing a sequence of images from a single-lens, 2D camera. Image analysis may be used to locate the projectile in the camera images, using motion detection and filters for the projectile's expected size and shape. A physics model may be used to calculate the projectile's trajectory as a function of its initial position and velocity (for example, just after impact with a golf club or bat). A camera projection transform may map this trajectory into predicted pixel locations, which may be compared to the observed projectile locations in the camera images. The projectile's trajectory may be estimated by finding initial conditions that minimize differences between observed and predicted pixel locations, using a nonlinear least squares solver for example. The method may be extended to multiple cameras.

Abstract: A system that measures a swing of a bat with one or more sensors and analyzes sensor data to create swing quality metrics. Metrics may include for example rotational acceleration, on-plane efficiency, and body-bat connection. Rotational acceleration measures the centripetal acceleration of the bat along the bat's longitudinal axis at a point early in the rotational part of the swing; it is an indicator of the swing's power. On-plane efficiency measures how much of the bat's angular velocity occurs around the swing plane, the plane spanned by the bat and the bat's sweet spot velocity at impact. Body-bat connection measures the angle between the bat and the body tilt axis, which is estimated from the trajectory of the hand position on the bat through the swing; an ideal bat-body connection is near 90 degrees. These three swing quality metrics provide a simple and useful characterization of the swing mechanics.

Abstract: A method that estimates the 3D trajectory of a projectile, such as a golf ball or baseball, by analyzing a sequence of images from a single-lens, 2D camera. Image analysis may be used to locate the projectile in the camera images, using motion detection and filters for the projectile's expected size and shape. A physics model may be used to calculate the projectile's trajectory as a function of its initial position and velocity (for example, just after impact with a golf club or bat). A camera projection transform may map this trajectory into predicted pixel locations, which may be compared to the observed projectile locations in the camera images. The projectile's trajectory may be estimated by finding initial conditions that minimize differences between observed and predicted pixel locations, using a nonlinear least squares solver for example. The method may be extended to multiple cameras.

Abstract: A method for analyzing sensor data from baseball swings (or swings in similar sports) that transforms data into a reference frame defined by the bat orientation and velocity at impact. The trajectory of the sweet spot of the bat is tracked through the swing, and is analyzed to generate metrics describing the swing. A two-lever model of the swing may be used to model the effects of body rotation and wrist rotation. Data may be analyzed to identify relevant events during the swing such as start of downswing, commit (wrist release), on-plane, peak bat speed, and impact. Illustrative swing metrics derived from the sweet spot trajectory, the swing plane reference frame, and the two-lever model include: forward bat speed, on-plane rotation, hinge angle at commit, hinge angle at impact, body rotation ratio, body tilt angle, and swing plane tilt angle.

Abstract: A method for analyzing sensor data from baseball swings (or swings in similar sports) that transforms data into a reference frame defined by the bat orientation and velocity at impact. The trajectory of the sweet spot of the bat is tracked through the swing, and is analyzed to generate metrics describing the swing. A two-lever model of the swing may be used to model the effects of body rotation and wrist rotation. Data may be analyzed to identify relevant events during the swing such as start of downswing, commit (wrist release), on-plane, peak bat speed, and impact. Illustrative swing metrics derived from the sweet spot trajectory, the swing plane reference frame, and the two-lever model include: forward bat speed, on-plane rotation, hinge angle at commit, hinge angle at impact, body rotation ratio, body tilt angle, and swing plane tilt angle.

Abstract: A method for analyzing sensor data from baseball swings (or swings in similar sports) that transforms data into a reference frame defined by the bat orientation and velocity at impact. The trajectory of the sweet spot of the bat is tracked through the swing, and is analyzed to generate metrics describing the swing. A two-lever model of the swing may be used to model the effects of body rotation and wrist rotation. Data may be analyzed to identify relevant events during the swing such as start of downswing, commit (wrist release), on-plane, peak bat speed, and impact. Illustrative swing metrics derived from the sweet spot trajectory, the swing plane reference frame, and the two-lever model include: forward bat speed, on-plane rotation, hinge angle at commit, hinge angle at impact, body rotation ratio, body tilt angle, and swing plane tilt angle.

Abstract: A method for analyzing sensor data from baseball swings (or swings in similar sports) that transforms data into a reference frame defined by the bat orientation and velocity at impact. The swing plane defined by these two axes provides a natural and robust reference frame for physically relevant measurements of swing characteristics. Illustrative swing metrics derived from swing plane reference frame data include: swing speed, defined as a rotational rate within the swing plane; total swing angle, defined as the angular change within the swing plane; and swing tempo, defined as the percentage of peak swing speed achieved halfway through the swing. Analyzing these metrics from multiple swings across multiple users identifies factors that contribute to peak performance. Metrics may be combined into multidimensional feature vectors that characterize a swing; these feature vectors may be used to group swings into swing styles or to match swings against similar players.

Abstract: A method for analyzing sensor data from baseball swings (or swings in similar sports) that transforms data into a reference frame defined by the bat orientation and velocity at impact. The swing plane defined by these two axes provides a natural and robust reference frame for physically relevant measurements of swing characteristics. Illustrative swing metrics derived from swing plane reference frame data include: swing speed, defined as a rotational rate within the swing plane; total swing angle, defined as the angular change within the swing plane; and swing tempo, defined as the percentage of peak swing speed achieved halfway through the swing. Analyzing these metrics from multiple swings across multiple users identifies factors that contribute to peak performance. Metrics may be combined into multidimensional feature vectors that characterize a swing; these feature vectors may be used to group swings into swing styles or to match swings against similar players.