I am trying to fit a helix to some 3 dimensional data using the nls function in R. I keep getting this error and I can’t figure out what is wrong with the syntax of my formula:

Error in str2lang(x) : :2:0: unexpected end of input 1: ~

Here is the code:

helix_model <- function(t, a, b) {
  data.frame(
    x = a * cos(t),
    y = a * sin(t),
    z = b * t
  )
}

data <- data.frame(
  x = c(1, 2, 3, 4, 5),
  y = c(2, 3, 4, 5, 6),
  z = c(0.1, 0.2, 0.3, 0.4, 0.5)
)

fit <- nls(
  cbind(x, y, z) ~ helix_model(t, a, b), 
  data = data,
  start = list(a = 1, b = 0.1)  # Initial values for parameters a and b
)

I am sure it is something simple that I am missing. Any help would be appreciated! Thank you!